UNIVERSITY  OF  CALIFORNIA,  SAN  DIEGO 


3  1822  03391  6719 


HODGSON, 


LIBRARY  ^ 

UNIVITRSITY  OP 
CALIFORNIA 
SAN  D1C60 


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presented  in  the 

LIBRARY 

UNIVERSITY  OF  CALIFORNIA  •  SAN  DIKGO 

by 

FRIENDS  OF  1  HE  LIHHARY 


Capt,    and  Mrs.    Ao    Wo    Borsum 

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UNIVERSITY  OP 
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UNIVERSITY  OF  CALIFORNIA   SAN  DIEGO 


3  1822  03391  6719 


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THE    STEEL    SQUARE. 


THE  CARPENTERS' 

Steel    Square, 


ITS     USES. 

BEING    A  DESCRIPTION  OF  THE     SQUARE,    AND     ITS     LSES    IN    OBTAINING 
THE  LENGTHS   AND   BEVELS   OF   ALL   KINDS   OF 

RAFTEKS,  HIPS,  GROINS,  BRACES.  BRACKETS,  PUR- 
LINS, COLLAR-BEAMS,  AND  JACK-RAFl'ERS; 

ALSO,    ITS    APPLICATION    IN    OBTAINING    THE    BEVELS    AND 

CUTS    FOR    HOPPERS,    SPRING    MOULDINGS,    OCTAGONS, 

STAIRS,    DIMINISHED    STILES,    ETC.,    ET^.,    ETC. 

ILLUSTRATED    BY    OVER    SEVENTY    WOOD-CUTS. 


BY 


FEED.    T.    HODGSON, 

Editor  of  the  "  Builder  and  Woodioorker'' 
Second   Edition.      Revised   and   Greatly   Enlarged. 


NEW  YORK: 
THE  INDUSTRIAL  PUBLICATION  COMPANY. 

1883. 

CoJ>)fright  Secured,  1880  and  1883,  I'y  John  PhtH. 


PREFACE  TO   SECOND  EDITION. 


The  rapid  disposal  of  the  first  edition  of  the  "Steel 
Square  and  Its  Uses,"  has  rendered  it  ineumbent  for  tlie 
publisher  to  issue  a  second  and  larger  edition  ;  and  recog- 
nizing this  condition,  in  connection  with  the  fact  that  the 
work  has  met  with  more  than  a  passing  favor  from  those 
who  make  daily  use  of  the  Steel  Square,  it  has  been 
deemed  necessary  to  make  the  present  edition  more 
useful  by  adding  a  number  of  solutions  of  mechanical 
problems  by  aid  of  the  instrument,  anl  other  matters 
that  will  render  the  work  more  valuable  to  the  operative 
mechanic. 

The  Author  has  reason  to,  and  does,  feel  pleased  at  the 
appreciation  the  working  mechanics  of  this  country  have 
evinced  for  this  work;  and  is  assured,  by  the  numerous 
letters,  and  other  indications  of  good  feeling  he  has  re- 
ceived on  all  hands,  that  the  present  enlargement  of  the 
work  has  not  been  made  unnecessarily  or  too  soon. 

Feeling  confident  that  the  additions  to  the  present  edi- 
tion will  commend  themselves  to  the  toiling  thousands 
who  have  daily  use  for  the  "Steel  Square,"  the  publishers 
send  the  enlarged  work  out  to  the  public  with  a  knowl- 
edge that  it  will  be  welcomed  by  those  who  are  most 
interested  in  the  subject  of  which  it  treats. 

New  York,  Jan.  1,  1883. 


I^REF^CE. 


Some  time  agro,  the  author  of  this  little  work  contributed  a  series 
of  papers  ou  the  STEEii  Square  and  Its  Uses,  to  the  Avierican 
Builder,  and  since  their  appearance,  he  has  received  hundreds  of 
letters  from  as  many  persons  residing  in  various  parts  of  the 
Unlte^l  States,  Canada,  Australia  and  New  Zealand,  in  which  the 
writers  requested  him  to  publish  the  papers  in  book  form.  Partly 
in  compliance  with  these  requests,  and  partly  at  the  solicitation 
of  personal  friends,  together  witli  a  knowledge  that  a  cheap  but 
thorough  work  of  the  kind,  woulrl  be  of  sei-vice  to  all  persons  who 
have  occasion  to  use  a  steel  square,  he  has  consented,  with  the  aid 
of  the  present  enterprising  publishers,  to  issue  the  work  as  now 
offered. 

It  is  only  of  late  years  that  American  workmen  have  begun 
fully  to  understand  the  capal)ilities  of  the  steel  square ;  and  even 
now,  oidy  a  few  of  tli(?  best  workmen  have  any  idea  of  what  can  be 
accomplished  with  it  when  in  skilful  hands. 

It  is  not  claimed  that  the  nlles  and  methods  shown  in  this  little 
work  are  either  new  or  original ;  they  have  been  known  to  advanced 
workmen  for  many  years  past ;  but  it  is  claimed  that  they  have 
never  before  been  brouglit  together  and  put  in  so  himdy  a  shape  as 


Vl  PREFACE. 

in  the  prericnt  book ;  imd  it  is  furtlior  claimed  tliat  many  of  the 
rules  herein  illustrated  and  explained,  have  never  appeared  in 
print  previous  to  tlic  publication  of  tho  papers  on  the  subject  in  the 
magazine  r(»fcrred  to  above. 

Should  this  little  volume  prove  of  service  to  the  man  who  toils 

with  axe,  saw  and  plane,  for  his  daily  bread,  and  profitable  to  the 

pul)lishers  who  risk  tlieir  mon(\v  on  its  publication,  it  will  have 

fulhlled  its  mission,  as  designed  by 

THEAUTHOil, 

New  York,  1880. 


OOI^TElSrTS, 


PAKT  I. 

PAGE 

reliminary        -----...     9 

Historical  and  Descriptive  -----        13 

Description  of  tlie  Square       -  -  -  -  -  -    16 

Board,  Planli  and  Scantling:  Jleasure     -  -  -  -         19 

Brace  Kule         -  -  -  -  -  -  -  -21 

Octagonal  Scale        ---....22 

Fence  for  Square  -  -  -  -  -  -  -24 

Application  of  Square        ----.--         25 

To  lay  out  Eafters        -  -  -  -  -  -  -28 

Hip  Rafters,  Cripph^s,  etc.  -  ....         33 

Backing  for  Hips  -  -  -  -  -  -  -    35 

Stairs  and  Strings    -------39 

Miscellaneous  Rule  i     -  -  -  -  -  -  -42 

Measurement  --  -....43 

Proportion  of  Circl  s-  -  -  -  -  -  -46 

Centering  Circles     -----..47 

How  to  Describe  an  Elli[)s>    -  -  -  -  .  -    48 

How  to  Describe  a  Parabola  -  -  -  .  .         49 

Bevels  for  Hoppers      -  -  -  -  -  .  -50 

Bisecting  Circles      -----..        51 

Cutting  Spring  Mouldings     -  -  -  -  -  -    54 


Vm  CONTENTS. 

PART  n. 

PAGE 

Theoretical  Rafters      -         -         -         -         -         -  -   57 

Bevels  and  Lengths  for  Hips,  Jacks  and  Purlins        -          -  58 

Divisions  of  Widths     -          -          -          -          -          -  -60 

Bisection  of  Angles            ......  eo 

Diminishing  Stiles        -          -          -          -          -  -    61 

PAR  r  HI. 

Octagons  ---------  62 

ToFind  the  Diagonal  of  a  Squiu<'           -           -           -           -  66 

Polygons  ---------  67 

Circles 68 

To  Lay  out  Angles        -           ------  70 

Bevels  of  Hoppers    -------  70 

Widths  of  Sides  and  Ends  ol' Ii()i)pcrs        -  -  -  .71 

Corner  Pieces  for  Hoppi'is           -----  73 

Roofing     ---------  73 

Lengths  and  Bevels  of  Hip-Rafters        -           -           -           -  73 

Backing  of  Hips 75 

Irregular  Hip  Roofs  -          -          -        .  -          -          -          -  75 

Trusses       ---------  77 

Diameter  of  Circles -  78 

Cutting  Equal  Mitres 80 

Theoretical  Lengths           ......  81 

PART  IV. 

Miscellaneous  Rules  and  Memoranda  -  -  -  -    83 

Hip  Roofs       --------     83-89 

Curved  Hip  Rafters -    91 

Hopper  Angles  -  -  -  -  -  -  -92 

Splayed  Gothic  Heads    - 95 


THE   CARPENTERS'   STEEL   SQUARE, 

AND   ITS   USES. 


PART  I. 

Preliminary. — There  is  nothing  of  more  importance  to 
a  young  man  who  is  learning  the  business  of  house-joinery 
and  carpeniiry,  than  that  he  should  make  himself  thoroughly 
conversant  with  the  capabilities  of  the  tools  he  employs.  It 
may  be  that,  in  some  of  the  rules  shown  in  this  work,  the 
result  could  be  attained  nmch  readier  with  other  aids  than 
the  square  ;  but  the  progressive  mechanic  will  not  rest  satis- 
fied with  one  method  of  performing  operations  when  others 
are  within  his  reach. 

In  the  hand  of  the  intelligent  mechanic  the  square  be- 
comes a  simple  calculating  machine  of  the  most  wonderful 
capacity,  and  by  it  he  solves  problems  of  the  kinds  continu- 
ally arising  in  mechanical  work,  which  by  the  ordinary 
methods  are  more  difficult  to  perform. 

The  great  improvement  which  the  arts  and  manufactures 
have  attained  within  the  last  fifty  years,  renders  it  essential 
that  every  person  engaged  therein  should  use  his  utmost 
exertions  to  obtain  a  perfect  knowledge  of  the  trade  he 


16  THE    STEEL    SQUARfi 

professes  to  follow.  It  is  not  enough,  nowadays,  for  a  per- 
son to  have  attained  the  character  of  a  good  workman ; 
that  phrase  implies  that  quantum  of  excellence,  which  con- 
sists in  working  correctly  and  neatly,  under  the  directions 
of  others.  The  workman  of  to-day,  to  excel,  must  under- 
stand the  principles  of  his  trade,  and  be  able  to  apply  them 
correctly  in  practice.  Such  an  one  has  a  decided  advan- 
tage over  his  fellow-workman  ;  and  if  to  his  superior  know- 
ledge he  possesses  a  steady  manner^  and  industrious  habits, 
his  efforts  cannot  fail  of  being  rewarded. 

It  is  no  sin  not  to  know  much,  though  it  is  a  great  one 
not  to  know  all  we  can,  and  put  it  all  to  good  use.  Yet, 
how  few  mechanics  there  are  who  will  know  all  they  can  ? 
Men  apply  for  employment  daily  who  claim  to  be  finished 
mechanics,  and  profess  to  be  conversant  with  all  the  ins 
and  outs  of  their  craft,  and  who  are  noways  backward  in 
demanding  the  highest  wages  going,  who,  when  tested,  are 
found  wanting  in  knowledge  of  the  simplest  formulas  of 
their  trade.  They  may,  perhaps,  be  able  to  perform  a  good 
job  of  work  after  it  is  laid  out  for  them  by  a  more  compe- 
tent hand ;  they  may  have  a  partial  knowledge  of  the  uses 
and  application  of  their  tools ;  but,  generally,  their  know- 
ledge ends  here.  Yet  some  of  these  men  have  worked  at 
this  trade  or  that  for  a  third  of  a  century,  and  are  to  all 
appearances,  satisfied  with  the  little  they  learned  when  they 
were  apprentices.  True,  mechanical  knowledge  was  not 
always  so  easily  obtained  as  at  present,  for  nearly  all  works 
on  the  constructive  arts  were  written  by  professional  archi- 
tects, engineers,  and  designers,  and  however  unexception- 
able in  other  respects,  they  were  generally  couched  in  such 
language,  technical  and  mathematical,  as  to  be  perfectly 


And  its  uses.  It 

Unintelligible  to  the  majority  of  workmen ;  and  instead  of 
acting  as  aids  to  the  ordinary  inquirer,  they  envelo])ed  in 
mystery  the  simplest  solutions  of  every-day  problems,  dis- 
couraging nine-tenths  of  workmen  on  the  very  threshold  ot 
inquiry,  and  causing  them  to  abandon  further  efforts  to 
master  the  intricacies  of  their  respective  trades. 

Of  late  years,  a  number  of  books  have  been  published, 
in  which  the  authors  and  compilers  have  made  commend- 
able efforts  to  simplify  matters  pertaining  to  the  arts  of  car- 
pentry and  joinery,  and  the  mechanic  of  to-day  has  not 
the  difficulties  of  his  predecessors  to  contend  with.  The 
■workman  of  old  could  excuse  his  ignorance  of  the  higher 
branches  of  his  trade,  by  saying  that  he  had  no  means  of 
acquiring  a  knowledge  of  them.  Books  were  beyond  his 
reach,  and  trade  secrets  were  guarded  so  jealously,  that  only 
a  limited  few  were  allowed  to  know  them,  and  unless  he  was 
made  of  better  stuff  than  the  most  of  his  fellow-workmen, 
he  was  forced  to  plod  on  in  the  same  groove  all  his  da}-s. 

Not  so  with  the  mechanic  of  to-day ;  if  he  is  not  well 
up  in  all  the  minutce  of  his  trade,  he  has  but  himself  to 
blame,  for  although  there  is  no  royal  road  to  knowledge, 
there  are  hundreds  of  open  ways  to  obtain  it ;  and  the 
young  mechanic  who  does  not  avail  himself  of  one  or  other 
of  these  ways  to  enrich  his  mind,  must  lack  energy,  or  be 
altogether  indifferent  about  his  trade,  and  may  be  put  down 
as  one  who  will  never  make  a  workman. 

I  have  thought  that  it  would  not  be  out  of  place  to  pre- 
face this  work  on  the  "  Steel  Square,"  with  the  foregoing 
remarks,  in  the  hope  that  they  may  stimulate  the  young 
mechanic,  and  urge  him  forward  to  conquer  what  at  best 
are  only   imaginary   difficulties.     A   willing  heart   and  a 


ti  THE    STEEL    SQUARE 

t 

clear  head  will  most  assuredly  win  honorable  distinction  in 
any  trade,  if  they  are  only  properly  used.  Indeed,  during 
an  experience  of  many  years  in  the  employment  and  su- 
perintendence of  mechanics  of  every  grade,  from  the  green 
"  wood-hagjjier "  to  the  finished  and  accomplished  work- 
man, I  have  invariably  discovered  that  the  finished  work- 
man was  the  result  of  persistent  study  and  application,  and 
not,  as  is  popuii;rly  supposed,  a  natural  or  spontaneous 
production.  It  it;  true  that  some  men  possess  greater 
natural  mechanical  abilities  than  others,  and  consequently 
a  greater  aptitude  i.-i  grasping  the  principles  that  underlie 
the  constructive  arts:  but,  as  a  rule,  such  men  are  not 
reliable;  they  may  i)c  expert,  equal  to  any  mechanical 
emergency,  and  quirk  it  mastering  details,  but  they  are 
seldom  thorough,  and  u  "ver  reliable  where  long  sustained 
efforts  are  required. 

The  mechanic  who  reaches  a  fair  degree  of  perfection  by 
experience,  study  and  application,  is  the  man  who  rises  to 
the  surface,  and  whose  steadiness  and  trustworthiness  force 
themselves  on  tlie  notice  of  employers  and  superinten- 
dents. I  have  said  this  in  order  to  give  encouragement 
to  those  young  niechanics  who  find  it  up-hill  work  to 
master  the  intricacies  of  the  various  arts  they  are  engaged 
in,  for  they  may  rest  assured  that  in  the  end  work  and 
application  will  be  sure  to  win ;  and  I  am  certain  that  a 
tliorough  stud\  of  the  steel  square  and  its  capabilities 
will  do  more  than  anything  else  to  aid  the  young  work- 
man in  uiastering  many  of  the  mechanical  difficulties  that 
will  confront  liim  from  time  to  time  in  his  daily  occupation. 

It  must  not  be  supposed  that  the  work  here  presented 
exhausts  the  subject.     'J'he  enterprising  mechanic  will  find 


AND    ITS    USES.  1 3 

*  - 

opportunity  for  using  the  square  in  the  solution  of  many 
problems  that  will  crop  up  during  his  daily  work,  and  the 
principles  herein  laid  down  will  aid  very  much  towards 
correct  solutions.  In  framing  roofs,  bridges,  trestle-work, 
and  constructions  of  timber,  the  Steel  Square  is  a  necessity 
to  the  American  carpenter ;  but  only  a  few  of  the  more  in- 
telligent workmen  ever  use  it  for  other  purposes  than  to 
make  measurements,  lay  off  the  mortices  and  tenons,  and 
square  over  the  various  joints.  Now,  in  framing  bevel 
work  of  any  description,  the  square  may  be  used  Avith 
great  advantage  and  profit.  Posts,  girts,  braces,  and  struts 
of  every  imaginable  kind  maybe  laid  out  by  this  wonderful 
instrument,  if  the  operator  will  only  study  the  plans  with  a 
view  of  making  use  of  his  square  for  obtaining  the  various 
bevels,  lengths  and  cuts  required  to  complete  the  work  in 
hand.  Tai^ering  structures — the  most  difficult  the  framer 
meets  with — do  not  contain  a  single  bevel  or  lengtli  that 
can  not  be  found  by  the  square  when  properly  applied,  and 
it  is  this  fact  I  wish  to  impress  on  my  readers,  for  it 
would  be  impossible,  in  this  work,  to  give  every  possible 
application  of  the  square  to  work  of  this  kind.  I  have, 
therefore,  only  given  such  examples  as  will  enable  any  one 
to  apply  some  one  of  them  to  any  work  in  hand. 

The  Square — Historical   and  Descriptive. — Doubtless, 

in  the  early  ages  of  mankintl,  when  solid  structures  be- 
came a  necessity,  the  want  of  an  instrument  similar  to  the 
square  must  have  been  felt  at  every  "  turn  and  corner," 
and  there  can  be  no  question  about  one  having  been  used — 
rude  and  imperfect  perhaps — in  erecting  the  first  square 
or  rectangular  building  that  was  ever  built  on  this  earth. 


14  THE    STEEL  SQUARE 

The  Greeks,  who  were  an  inventive  people,  and  who 
were  apt  to  ascribe  to  themselves  more  credit  than  was 
really  their  due,  in  the  way  of  inventions  and  discoveries, 
lay  claim  to  be  the  inventors  of  the  instrument.  Pliny 
says  that  Theodorus,  a  Greek  of  Samos,  invented  the 
square  and  level.  Theodorus  was  an  artist  of  some  note, 
but  it  is  evident  that  the  square  and  level,  in  some  form 
or  other,  were  used  long  before  his  time,  even  in  his  own 
country,  for  some  of  the  finest  temples  in  Athens  and  other 
Grecian  cities,  had  been  built  long  before  his  time;  and 
the  Pyramids  of  Egypt  were  hoary  with  age  when  he  was 
in  swaddling  clotlis.  Indeed,  the  "  square,"  as  a  construc- 
tive tool,  must  of  necessity  have  found  a  place  in  the 
"  kit "  of  the  earliest  builders.  Evidences  of  its  presence 
have  been  found  in  tlie  ruins  of  pre-historic  nations,  and 
are  abundant  in  the  remains  of  ancient  Petra,  Nineveh, 
Babylon,  Etruria,  and  India.  South  American  ruins  of 
great  antiquity  in  Brazil,  Peru,  and  other  places,  show  that 
the  unknown  races  that  once  inhabited  the  South  American 
Continent,  were  familiar  with  many  of  the  uses  of  the 
square'.  Egypt,  however,  that  cradle  of  all  the  arts,  fur- 
nishes us  with  the  most  numerous,  and,  perhaps,  the  most 
ancient  evidences  of  the  use  of  the  square;  paintings  and 
inscriptions  on  the  rock-cut  tombs,  the  temples,  and  other 
works,  showing  its  use  and  application,  are  plentiful.  In 
one  instance,  a  whole  "  kit "  of  tools  was  found  in  a  tomb 
at  Thebes,  which  consisted  of  mallets,  hammers,  bronze 
nails,  small  tools,  drills,  hatchets,  adzes,  squares,  chisels, 
etc.;  one  bronze  saw  and  one  adze  have  the  name  of 
Thothmes  III.,  of  the  i8th  dynasty,  stamped  on  their 
blades,  showing  that  they  were   made  nearly  3,500  years 


AND    ITS    USES.  1 5 

ago.  The  constructive  and  decorative  arts  at  that  time 
were  in  their  zenith  in  Egypt,  and  must  have  taken  at  least 
I, GOO  years  to  reach  that  stage.  Consequendy,  the 
square  must  have  been  used  by  workmen  of  that  country, 
at  least,  four  thousand  years  ago. 

The  British  Museum  contains  many  tools  of  pre-historic 
ongin,  and  the  square  is  not  the  least  of  them.  Hercu- 
laneum  and  Pompeii  contribute  evidences  of  the  importance 
of  this  useful  tool.  On  some  of  the  paintings  recently  dis- 
covered in  those  cities,  the  diiTerent  artisans  can  be  seen  at 
home  in  their  own  workshops,  with  their  work-benches, 
saw-horses,  tools,  and  surroundiiigs,  much  about  the  same 
as  we  would  find  a  small  carpenter  shop  of  to-day,  wliere 
all  the  work  is  done  by  hand ;  the  only  difference  being  a 
change  in  the  form  of  some  of  the  tools,  which,  in  some 
instances,  had  been  better  left  as  these  old  workmen  de- 
vised them. 

It  can  make  no  difference,  however,  to  the  modern 
workman,  as  to  when  or  where  the  square  was  first  used ; 
suftice  to  know,  that,  at  present,  we  have  squares  im- 
mensely superior  to  anything  known  to  the  ancients,  and 
it  may  be  added,  that  so  perfect  has  the  machinery  for 
the  manufacture  of  steel  squares  become,  that  a  defective 
tool  is  now  the  exception.  Of  course  this  relates  to  the 
products  of  manufacturers  of  repute,  and  not  to  the  cheap 
squares,  or  to  those  said  to  be  "  first-class,"  that  were  made 
ten  or  fifteen  years  ago.  The  tool  we  recommend  else- 
where is  the  best  made,  both  as  to  quality  of  material, 
accuracy  of  workmanship,  and  amount  cf  useful  matter  on 
its  faces. 


1 6  THE    STEEL   SQUARE 

Description  of  the  Square.— In  the  foregoing  sketch  I 
have  given  a  few  hints  as  to  the  kind  of  square  to  purchase 
when  it  is  necessary  to  buy ;  in  many  cases,  however,  this 
book  will  find  its  way  into  the  hands  of  mechanics  and 
others,  who  will  have  old  and  favorite  squares  in  their 
chests  or  works^^  ops,  and  who  will  not  care  to  dispose  of 
a  "  well-tried  ,riend  "  for  the  purpose  of  filling  its  place 
with  another,  simply  because  I  have  recommended  it.  To 
these  workmen  I  would  say  that  I  do  not  advise  a  change, 
provided  the  old  square  is  true,  and  the  inches  and  sub- 
divisions are  properly  and  accurately  defined.  I  wish  it 
distinctly  understood  that  old  squares,  if  true,  and  marked 
with  inches  and  sub-divisions  of  inches,  will  perform  nearly 
every  solution  presented  in  this  book. 

The  lines  and  figures  formed  on  the  squares  of  different 
make,  sometimes  vary,  both  as  to  their  position  on  the 
square,  and  their  mode  of  application,  but  a  thorough 
understanding  of  the  application  of  the  scales  and  lines 
shown  on  any  first-class  tool,  will  enable  the  student  to 
comprehend  the  use  of  the  lines  and  figures  exhibited  on 
other  first-class  squares. 

To  insure  good  results,  it  is  necessary  to  be  careful  in 
the  selection  of  the  tool.  The  blade  of  the  square  should 
be  24  inches  long,  and  two  inches  wide,  and  the  tongue 
from  14  to  18  inches  long  and  ij4  inches  wide.  The 
tongue  should  be  exactly  at  riglit  angles  with  the  blade, 
or  in  other  words  the  "square"  should  be  perfectly  square. 

To  test  this  question,  get  a  board,  about  12  or  14  inches 
•wide,  and  four  feet  long,  dress  it  on  one  side,  and  true  up  one 
edge  as  near  straight  as  it  is  possible  to  make  it.  Lay  the 
board  on  the  bench,  with    the   dressed   side  up,  and  the 


AND    ITS    USES.  l? 

trued  edge  towards  you,  then  apply  the  square,  with  the 
blade  to  the  left,  and  mark  across  the  prepared  board  with 
a  penknife  blade,  pressing  close  againsi  the  edge  of  the 
tongue ;  this  process  done  to  your  satisfaction,  reverse  the 
square,  and  move  it  until  the  tongue  is  close  up  to  the 
knife  mark;  if  you  find  tliat  the  edge  of  the  tongue  and 
mark  coincide,  it  is  proof  tliat  the  tool  is  correct  enough 
for  your  purposes. 

This,  of  course,  relates  to  the  inside  edge  of  the  blade, 
and  the  outside  edge  of  the  tongue.  If  these  edges  should 
not  be  straight,  or  should  not  prove  perfectly  true,  they 
should  be  filed  or  ground  until  they  are  straight  and  true. 
The  outside  edge  of  the  blade  should  also  be  "  trued  "  up 
and  made  exactly  parallel  with  the  inside  edge,  if  such 
is  required.  The  same  process  shuuld  be  gone  through 
on  the  tongue.  As  a  rule,  squares  made  by  firms  of 
repute  are  perfect,  and  require  no  adjusting;  nevertheless, 
it  is  well  to  make  a  critical  examination  before  purchasing. 

The  next  thing  to  be  considered  is  the  use  of  the  figures, 
lines,  and  scales,  as  exhibited  on  the  square.  It  is  sup- 
posed that  the  ordinary  divisions  ant-  sub-divisions  of  the 
inch,  into  halves,  quarters,  eigliths,  and  sixteenths  are  un- 
derstood by  the  student;  and  that  he  also  understands 
how  to  use  that  part  of  the  square  that  is  sub-divided  into 
twelfths  of  an  inch.  This  being  conceded,  we  now  proceed 
to  describe  the  various  rules  as  shown  on  all  good  squares; 
but  before  proceeding  further,  it  may  not  be  out  of  place 
to  state,  that  on  the  tool  recommended  in  this  book,  one 
edge  is  subdivided  into  thirty-seconds  of  an  inch. 

This  fine  sub-division  will  be  found  very  useful,  particu- 
larly so  when  used  as  a  scale  to  measure  drawings  made  in 


THE    STEEL    SQUARE 


lialf,  quarter,  one-eighth,  or  one-sixteenth  of  an  inch  to  the 
foot. 

I  now  refer  the  reader  to  the  square  shown  in  the 
Frontispiece.  It  is  the  one  recommended  in  the  foregoing 
pages,  and  is  the  most  complete  square  in  the  market,  and 
manufactured,  I  beheve,  but  by  one  firm.  It  is  known  to 
the  trade  as  No.  loo,  and  this  number  Avill  be  found 
stamped  always  on  the  face  side  of  the  square  at  the  junc- 
tion of  the  tongue  and  blade.  The  following  instructions 
refer  to  the  Frontispiece  and  accompanying  cuts. 

The  diagonal  scale  is  on  the  tongue  at  the  junction  with 
blade.  Fig.  i,  and  is  for  taking  off  hundredths  of  an  inch. 
The   lengths  of  the  lines  between    the  diagonal  and  the 


Fig.  2  a. 

perpendicular  are  marked  on  the  latter.  Primary  divisions 
are  tenths,  and  the  junction  of  the  diagonal  lines  with  the 
longitudinal  parallel  lines  enables  the  operator  to  obtain 
divisions  of  one  hundredth  part  of  an  inch ;  as,  for  example, 
if  we  wish  to  obtain  twenty-four  hundredths  of  an  inch,  we 
place  the  compasses  on  the  "  dots  "  on  the  fourth  parallel 
line,  which  covers  two  primary  divisions,  and  a  fraction,  or 


AND    ITS    USES.  I9 

four-tenths,  of  the  third  primary  division,  which  added 
together  makes  twenty-four  hundredths  of  an  inch.  Again, 
if  we  wish  to  obtain  five  tenths  and  seven  hundredths,  we 
operate  on  the  seventh  Hne,  taking  five  primaries  and  the 
fraction  of  the  sixth  where  the  diagonal  intersects  the 
parallel  line,  as  shown  by  the  "  dots,"  on  the  compasses, 
and  this  gives  us  the  distance  required. 

The  use  of  this  scale  is  obvious,  and  needs  no  further 
explanation. 

Fig.  2  a  shows  the  position  of  the  "  dots  "  or  "  points  " 
referred  to  in  the  foregoing  example  of  the  use  of  the 
diagonal  scale. 

Board,  Plank  and  Scantling  Measure.— Perhaps,  with 
the  single  exception  of  the  common  inch  divisions  on  the 
square,  no  set  of  figures  on  the  instrument  will  be  found 
more  useful  to  the  active  workman  than  that  known  as  the 
board  rule.  A  thorough  knowledge  of  its  use  may  be  ob- 
tained by  ten  minutes'  study,  and,  when  once  obtained,  is 
always  at  hand  and  ready  for  use. 

The  following  explanations  are  deemed  sufficiently  clear 
to  give  the  reader  a  full  knowledge  of  the  workings  of  the 
rule.  If  we  examine  Fig.  2,  in  the  Frontispiece,  we  will 
find  under  the  figure  12,  on  the  outer  edge  of  the  blade, 
where  the  length  of  the  boards,  plank,  or  scantling  to  be 
measured,  is  given,  and  the  answer  in  feet  and  inches  is  found 
under  the  inches  in  width  that  the  board,  etc.,  measures. 
For  example,  take  a  board  nine  feet  long  and  five 
inches  wide;  then  under  the  figure  12,  on  the  second 
line  will  be  found  the  figure  9,  which  is  the  length 
of    the    board;    then   run   along  this  line   to   the   figure 


20  THE    STEEL    SQUARE 

directly  under  the  five  inches  (the  width  of  the  board),  and 
we  find  three  feet  nine  inches,  which  is  the  correct  answer 
in  "  board  measure."  If  the  stuff  is  two  inches  thick,  the 
sum  is  doubled  ;  if  three  inches  tliick,  it  is  trebled,  etc.,  etc. 
If  the  stuff  is  longer  than  any  figures  shown  on  the  square, 
it  can  be  measured  by  dividing  and  doubling  the  result. 
Tins  rule  is  calculated,  as  its  name  indicates,  for  board 
measure,  or  for  surfaces  i  inch  in  thickness.  It  may  be 
advantageously  used,  however,  upon  timber  by  multiplying 
the  result  of  the  face  measure  of  one  side  of  a  i:)iece  by  its 
depth  in  inches.  To  illustrate,  suppose  it  be  re  juired  to 
measure  a  piece  of  timber  25  feet  long,  10  x  14  inches  in 
size.  For  the  length  we  will  take  12  and  13  feet.  For 
the  width  we  will  take  10  inches,  and  multiply  the  result 
by  I  A.     By  the  rule  a  board   12  feet  long  and  10  incbe<5 


Fig-  3. 

wide  contains  10  feet,  and  one  13  feet  long  and  10  inches 

wide,  10  feet  to  inches.  Therefore,  a  board  25  feet  long 
and  10  inches  wide  must  contain  20  feet  and  10  inches. 
In  the  timber  above  described,  hoAvever,  we  have  what  is 
equivalent  to  14  such  boards,  and  therefore  we  multiply 
this  result  by  14,  which  gives  291  feet  and  8  inches,  the 
board  measure. 

The  "  board  measure,"  as  shown  on  the  portion  of  the 


AND    ITS    USES. 


it 


square,  Fig.  3,  gives  the  feet  contained  in  each  board  ac- 
cording to  its  length  and  width.  This  style  of  figuring 
squares,  for  board  measure,  is  going  out  of  date,  as  it  gives 
the  answer  only  in  feet. 


t'ly,.   j  X. 


Fig.  3  rt!  shows  the  method  now  in  use  for  board  measure. 
This  shows  the  correct  contents  in  feet  and  inclies.  It  is 
a  portion  of  the  blade  of  the  square,  as  shown  at  Fig.  2,  on 
the  Frontispiece. 

Brace  Rule. — The  "brace  rule"  is  always  placed  on  the 
tongue  of  the  square,  as  shown  in  the  central  space  at  x, 
Fig.  I. 

This  rule  is  easily  understood  ;  the  figures  on  the  left  of 
the  line  represent  the  "  run  "  or  the  length  of  two  sides  of  a 
right  angle,  while  the  figures  on  the  right  represent  the 
exact  length  of  the  third  side  of  a  right-angled  triangle,  in 
inches,  tenths,  and  hundredths.  Or,  to  explain  it  in  another 
way,  the  equal  numbers  placed  one  above  the  other,  may 
be   considered  as  representing  the  sides  of  a  square,  and 


22  THE    STEEL   SQUARE 

the  third  number  to  the  right  the  length  of  the  diagonal  of 
that  square.  Thus  the  exact  length  of  a  brace  from  point 
to  point  having  a  run  of  ^^  inches  on  a  post,  and  a  run  of 
the  same  on  a  girt,  is  46-67  inches.  The  brace  rule  varies 
somewhat  in  the  matter  of  the  runs  expressed  in  different 
squares.  Some  squares  give  a  few  brace  lengths  of  which 
the  runs  upon  the  post  and  beam  are  unequal. 

Octagonal  Scale. — The  "  octagonal  scale,"  as  shown  on 
the  central  division  of  the  upper  portion  of  blade,  is  on  the 
opposite  side  of  the  square  to  the  "  brace  rule,"  and  runs 
along  the  centre  of  the  tongue  as  at  s  s.     Its  use  is  as  fol- 
lows :    Suppose  a  stick  of  timber  ten  inches  square.     Make 
a  centre  line,  which  will  be  five  inches  from  each  edge  ;  set 
a  pair  of  compasses,  putting  one  leg  on  any  of  the  main 
divisions  shown  on  the  square  in  this  scale,  and  the  other 
leg  on  the  tenth  subdivision.     This   division,  pricked  off 
from  the  centre  line  on  the  timber  on   each  side,  Avill  give 
the    points  for  the  gauge-lines.     Gauge  from    the  corners 
both  ways,  and  the  lines  for  making  the  timber  octagonal 
in  its  section  are  obtained.     Always  take  the  same  number 
of  spaces  on  your  compasses  as  the  timber  is  inches  square 
from   the   centre   line.     Thus,  if  a  stick  is  twelve  inches 
square,  take  twelve  spaces  on   the  compasses ;  if  only  six 
inches  square,  take  six  spaces  on  the  compasses,  etc.,  etc. 
The  rule  always  to  be  observed  is  as  follows  :    Set  ofif  from 
each  side  of  the  centre  line  upon  each  face  as  many  spaces 
by  the  octagon  scale  as  the  timber  is  inches  square.     For 
timbers  larger  in  size  than  the  number  of  divisions  in  the 
scale,  the  measurements  by  it  may  be  doubled  or  trebled, 
as  the  case  may  be. 


AND    ITS    USES. 


23 


The  diagram,  Fig.  4  a,  shows  the  application  of  the  rule 
applied  to  the  end  of  a  stick  of  timber  or  on  a  plane  sur- 
face. Let  B  c  D  E,  be  the  square  equal  to  six  inches  on  a 
side.     Draw  the  centre  lines,  b  c  and  D  e,  then  with  the 


e 

/ 

\ 

5 

\ 

/ 

4: 

Fig.  A,a- 

dividers  take  from  the  scale  six  parts,  and  lay  off  tliis  dis- 
tance from  the  centre  of  each ;  as  bi,  b  2,  e  3  and  e  4, 
C  5  and  c  6,  D  7  and  d  8.  Draw  lines  from  i  to  8,  2  to  3, 
4  to  5,  6  to  7,  and  the  octagon  figure  is  complete. 

A  rule  for  laying  off  octagons  is  figured  on  nearly  all 
carpenters'  two-foot  rules,  marked  off  from  the  inner  edges 
of  the  rule;  one  set  of  figures  is  denoted  by  the  letter  e, 
another  set  is  denoted  by  the  letter  m.  That  set  marked 
E  measures  the  distance  from  the  edge  of  the  square  to  the 
points  indicated  in  the  diagram,  by  the  figures  i,  2,  3,  4, 
etc.  The  set  marked  m  is  used  for  finding  the  points  i,  2, 
3,  4,  etc.,  by  measuring  from  the  middle  or  centre  lines,  b, 

E,  C,  D. 

I  have  now  fully  described  all  the  Hnes,  figures,  and 
scales  that  are  usually  found  on  the  better  class  of  squares 
now  in  use ;  but,  I  may  as  well  here  remark  that  there  are 
squares  in  use  of  an  inferior  grade,  that  are  somewhat  dif- 


24  THE     STEEL    SQUARE 

ferently  figured.  These  tools,  however,  are  such  as  can 
not  be  recommended  for  the  purposes  of  the  scientific 
carpenter  or  joiner. 

Fence. — A  necessary  appendage  to  the  steel  square  in 
solving  mechanical  problems,  is,  what  I  call,  for  the  want 
of  a  better  name,  an  adjustable  fence.  This  is  made  out 
of  a  piece  of  black  walnut  or  cherry  2  inches  wide,  and  2 
feet  10  inches  long  (being  cut  so  that  it  will  pack  in  a  tool 
chest),  and  i^  inches  thick;  run  a  gauge  line  down  the 
centre  of  both  edges;  this  done,  run  a  saw  kerf  cutting 
down  these  gauge  lines  at  least  one  foot  from  each  end, 
leaving  about  ten  inches  of  solid  wood  in  the  .entre  of 
fence.  We  now  take  our  square  and  insert  the  blade  in  the 
saw  kerf  at  one  end  of  the  fence,  and  the  tongue  in  the 
kerf,  at  the  other,  the  fence  forming  the  third  side  of  a 
right-angle  triangle,  the  blade  and  the  tongue  of  the  square 
forming  the  other  two  sides.     A  fence  may  be  made  to  do 


Fig. 


pretty  fair  service,  if  the  saw  kerf  is  all  cut  from  one  end 
as  shown  at  Fig.  4.  The  one  first  described,  however,  will 
be  found  the  most  serviceable.  The  next  step  will  be  to 
make  some  provision  for  holding  the  fence  tight  on  the 
square  ;  this  is  best  done  by  putting  a  No.  10  1 1^  inch 
screw  in  each  end  of  the  fence,  close  up  to  the  blade  and 
tongue ;  having  done  this,  we  are  ready  to  proceed  to  busi- 
ness. 


AND     ITS     USES.  25 

Application. — The  fence  being  made  as  desired,  in  eidier 
of  the  methods  mentioned,  and  adjusted  to  the  sc^uare,  work 
can  be  commenced  forthwith. 

The  first  attempt  will  be  to  make  a  pattern  for  a  brace, 
for  a  four-foot  "  run."  Take  a  piece  of  stuff  already  pre- 
pared, six  feet  long,  four  inches  wide  and  half-inch  thick, 
gauge  it  three-eighths  from  jointed  edge. 

Take  the  square  as  arranged  at  Fig.  5,  and  place  it  on 
the  prepared  stuff  as  shown  at  Fig.  6.  Adjust  the  square 
so  that  the  twelve-inch  lines  coincide  exactly  with  the 
gauge  line  o,  o,  o,  c.  Hold  the  square  firmly  in  the  posi- 
tion now  obtained,  and  slide  the  fence  up  the  tongue  and 
blade  until  it  fits  snugly  against  the  jointed  edge  of  the 
prepared  stuff,  screw  the  fence  tight  on  the  square,  and  be 
sure  that  the  12  inch  marks  on  both  the  blade  and  the 
tongue  are  in  exact  position  over  the  gauge-line. 

I  repeat  this  caution^  because  the  successful  completion 
of  the  work  depends  on  exactness  at  this  stage. 

We  are  now  ready  to  lay  out  the  pattern.  Slide  the 
square  to  the  extreme  left,  as  shown  on  the  dotted  lines  at 
X,  mark  with  a  knife  on  the  outside  edges  of  the  square, 
cutting  the  gauge-line.  Slide  the  square  to  the  right  until 
the  12  inch  mark  on  the  tongue  stands  over  the  knife  mark 
on  the  gauge -line  ;  mark  the  right-hand  side  of  the  square 
cutting  the  gauge-line  as  before,  repeat  the  process  four 
times,  marking  the  extreme  ends  to  cut  off,  and  we  have 
the  length  of  the  brace  and  the  bevels. 

Square  over,  with  a  try  square,  at  each  end  from  the 
gauge-line,  and  we  have  the  toe  of  the  brace.  The  lines, 
s,  s,  shown  at  the  ends  of  the  pattern,  represent  the  tenons 
that  are  to  be  left  on  the  braces.     This  pattern  is  now  com- 


26 


THE     STEEL    SQUARE 


V' 


\,> 


AND    Its    USES.  27 

piete ;  to  make  it  handy  for  use,  however,  nail  a  strip  2  inches 
wide  on  its  edge,  to  answer  for  a  fence  as  shown  at  K,  and 
the  pattern  can  then  be  used  either  side  up. 

The  cut  at  Fig.  7,  shows  the  brace  in  position,  on  a  re- 
duced scale.  The  principle  on  which  the  square  works  in 
the  formation  of  a  brace  can  easily  be  understood  from  this 
cut,  as  the  dotted  lines  show  the  position  the  square  was  in 
when  the  pattern  was  laid  out. 

It  may  be  necessary  to  state  that  the  "  square,,"  as  now 
arranged,  will  lay  out  a  brace  pattern  for  any  length,  if  thfc 
angle  is  right,  and  the  run  equal.  Should  the  brace  be  of 
great  length,  however,  additional  care  must  be  taken  in  the 
adjustment  of  the  square,  for  should  there  be  any  departure 
from  truth,  that  departure  will  be  repeated  every  time  the 
square  is  moved,  and  where  it  would  not  affect  a  short  run,  it 
might  seriously  affect  a  long  one. 

To  lay  out  a  pattern  for  a  brace  where  the  run  on  the 
beam  is  three  feet,  and  the  run  down  the  post  four,  proceed 
as  follows : 

Prepare  a  piece  of  stuff,  same  as  the  one  operated  on  for 
four  feet  riui;  joint  and  gauge  it.  Lay  the  square  on  the 
left-hand  side,  keep  the  12  inch  mark  on  the  tongue,  over 
the  gauge-line,  place  the  9  inch  mark  on  the  blade,  on  the 
gauge-line,  so  that  the  gauge-line  forms  the  third  side  of  a 
right-angle  triangle,  the  other  sides  of  which  are  nine  and 
twelve  inches  respectively. 

Now  proceed  as  on  the  former  occasion,  and  as  shown 
at  Fig.  8,  taking  care  to  mark  the  bevels  at  the  extreme 
ends.  The  dotted  lines  show  the  positions  of  the  square, 
as  the  pattern  is  being  laid  out. 

Fig.  9  shows  the  brace  in  position,  the  dotted  lines  show 


>8 


THE     STEEL    SQUARE 


where  the  square  was  placed  on  the  pattern.  It  is  well  tO 
thoroughly  understand  the  method  of  obtaining  the  lengths 
and  bevels  of  irregular  braces.  A  little  study,  will  soon 
enable  any  person  to  make  all  kmds  of  braces. 

If  we  want  a  brace  with 
a  two  feet  run,  and  a  four 
feet  run,  it  must  be  evident 
that,  as  two  is  the  half  of 
four,  so  on  the  square  take 
1 2  inches  on  the  tongue,  and 
6  inches  on  the  blade,  apply 
four  times,  and  we  have  the 
length,  and  the  bevels  of  a 
brace  for  this  run. 

For  a  tliree  by  four  feet 
"  run,  take  1 2  inches  on  the 
'^  tongue,  and  9  inches  on  the 
blade,  and  apply  four  times, 
because,  as  3  feet  is  ^  of  four 
feet,  so  9  inches  is  ^  of  12 
inches. 

Rafters. — Fig.  10  shows 
a  plan  of  a  roof,  having 
twenty-six  feet  of  a  s})an. 

The  span  of  a  roof  is  the 
distance  over  the  wall  plates 
measuring  from  A  to  A,  as  shown  in  Fig.  10.  It  is  also 
the  extent  of  an  arch  between  its  abutments. 

There  are  two  rafters  shown  in  position  on  Fig.  10.    The 
one  on  the  left  is  at  an  inclination  of  quarter  pitch,  and 


in 


AND     ITS     USES. 

marked  B,  and  the  one  on  tlie  right, 
marked  C,  has  an  incHnation  of  one-third 
pitch.  These  angles,  or  incHnations  rather, 
are  called  quarter  and  third  pitch,  respec-  'C\g 

tively,  because  the  height  from  level  of  wall 
plates  to  ridge  of  roof  is  one-quarter  or  one- 
third  the  width  of  building,  as  the  case 
may  be. 

At  Fig.  1 1,  the  rafter  B  is  shown  drawn  to 
a  larger  scale;  you  will  notice  that  this  rafter 
is  for  quarter  pitch,  and  for  convenience,  it  is 
supposed  to  consist  of  a  piece  of  stuff  2 
inches  by  6  inches  by  1 7  feet.  That  portion 

of  the  rafter  that  projects  over  the  wall  of  the  ^ 

PI 
building,  and  forms  the  eve,  is  three  or  more       -^    -^ 
r         .  .  ~      -f> 

inches  in  width,  just  as  we  please.     The 

length  of  the  projecting  piece  in  this  case  is 

one  foot — it  may  be  more  ji:  less  to  suit  the 

eve,  but  the  line  must  continue  from  end  to 

end  of  the  rafter,  as  shown  on  the  plan,  and 

we  will  call  this  line  our  working  line. 

We    are    now    ready    to    lay    out    this 

rafter,  and  will  proceed   as    follows :  We 

adjust  the  fence  on  the  square  the  same  as 

for  braces,   press  the  fence  firmly  against 

the  top  edge  of  rafter,  and  place  the  figure 

12  inches    on   the  left-hand  side,  and  the 

figure  6  in  on  the  right-hand  side,  directly 

over  the  working  lipe,    as  shown  on  the 

plan.     Be   very    exact  about    getting   the 

figures  on  the  line,  for  the  quality  ot  the 


29 


* 


3q  THE     STEEL    SQUARE 

work,  depends  much  on  this;  when  you  are  satisfied  that 
you  are  right,  screw  your  fence  tight  to  the  square.  Com- 
mence at  No.  I  on  the  left,  and  mark  off  on  the  working 
hne;  then  shde  your  square  to  No.  2,  repeat  the  marking 
and  cont'nue  the  process  until  you  have  measured  off 
thirteen  spaces,  the  same  as  shown  by  the  dotted  lines  in 
the  drawing.  The  last  line  on  the  right-hand  side  will  be 
the  plumb  cut  of  the  rafter,  and  the  exact  length  required. 
It  will  be  noticed  that  tho  square  has  been  applied  to  the 
timber  thirteen  times. 

The  reason  for  this  is,  that  the  building  is  twenty-six  feet 
wide,  the  half  of  which  is  thirteen  feet,  the  distance  that 
one  rafter  is  expected  to  reach,  so,  if  the  building  was  thirty 
feet  wide,  Ave  should  be  obliged  to  apply  the  square  fifteen 
times  instead  of  thirteen.  We  may  take  it  for  granted, 
then,  that  in  all  cases  where  this  method  is  employed  to 
obtain  tne  lengths  and  bevels,  or  cuts  of  rafters,  we  must 
apply  the  square  half  as  many  times  as  there  are  feet  in  the 
width  of  the  building  being  covered.  If  the  roof  to  be 
covered  is  one-third  pitch,  all  to  be  done  is  to  take  12 
inches  on  one  side  of  the  square  and  8  inches  on  the  other, 
and  operate  as  for  quarter  pitch. 

We  shall  frequently  meet  with  roofs  much  more  acute 
than  the  ones  shown,  but  it  will  be  easy  to  see  how  they 
can  be  managed.  For  instance,  where  the  rafters  are  at 
right-angles  to  each  other,  apply  the  square  the  same  as 
for  braces  of  equal  run,  that  is  to  say,  keep  the  12  mark  on 
the  blade,  and  the  12  mark  on  the  tongue,  on  the  working 
line.  When  a  roof  is  more  acute,  or  "steeper"  than  a 
right-angle,  take  a  greater  figure  than  twelve  on  one  side 
of  the  square,  and  twelve  on  the  other, 


AND     ITS    USES. 


31 


Whenever  a  drawing  of  a  roof  is  to  be  followed,  we  can 
soon  find  out  how  to  employ  the  f  ]uare,  by  laying  it  on 
the  drawing,  as  shown  in  Fig.  12.  Of  course,  something 
depends  on  the  scale  to  which  the  drawing  is  made.  If 
any  of  the  ordinary  fractions 
of  an  inch  are  used,  the  intelli- 
gent workman  will  have  no 
difficulty  in  discovering  what 
figures  to  make  use  of  to  get 
the  "  cuts "  and  length  de- 
sired. 

Sometimes  there  may  be  a 
fraction  of  a  foot  in  this  divis- 
ion ;  when  such  is  the  case,  it 
can  be  dealt  with  as  follows :  o 
suppose  there  is  a  fraction  of  « 
a  foot,  say  8  inches,  the  half 
of  which  would  be  4  inches, 
or  ^  of  a  foot ;  then,  if  the 
roof  is  quarter  pitch,  all  to  be 
done  is  to  place  the  square, 
with  the  4  inch  mark  on  the 
blade,  and  the  2  inch  mark  on 
the  tongue,  on  the  centre  line 
of  the  rafter,  and  the  distance 
between  these  points  is  the 
extra  length  required,  and  the  line  down  the  tongue  is  the 
bevel  at  the  point  of  the  rafter.  On  Fig.  13,  is  shown 
an  application  of  this  method.  All  other  pitches  and  frac- 
tions can  be  treated  in  this  manner  without  overtaxing  the 
ingenuity  of  the  workman, 


32 


THE    STEEL    SQUARE 


Fi&  r.^. 


Fig.  14. 


AND     ITS     USES. 


33 


Sufficient  has  been  shown  to  enable  the  student,  if  he 
has  mastered  it,  to  find  the  lengths  and  bevels  of  any  com- 
mon rafter ;  therefore,  for  the  present,  we  will  leave  saddle 
roofs,  and  try  what  can  be  done  with  the  square  in  de- 
termining the  lengths  and  bevels  of  "  hips,"  valleys,  and 
cripples. 


Fig.  15. 

Fig.  1 4  shows  how  to  get  bevels  on  the  top  end  of  vertical 
boarding,  at  the  gable  ends,  suitable  for  the  quarter  pitch 
at  Fig.  10. 

At  Fig.  15,  is  shown  a  method  for  finding  the  bevel  for 
horizontal  boarding,  collar  ties,  etc. 


Hip  Rafters. — Fig.  16,  is  supposed  to  be  the  pitch  of  a 
roof  furnished  by  an  architect,  \7ith  the  square  applied  to 
the  pitch.     The  end  of  the  long  blade  must  only  just  enter 


34 


THE    STEEL    SQUARE 


SoOARESErTO 

HipRafterto 

GET  LCfJCTH. 


Fisn. 


AND     ITS    USES.  35 

the  tence,  as  shown  in  the  drawing,  and  the  short  end  must 
be  adjusted  to  the  pitch  of  the  roof,  whatever  it  may  be. 
Fig.  1 7  shows  the  square  set  to  the  pitch  of  the  hip  rafter. 
The  squares  as  set  give  the  plumb  and  level  cuts.  Fig.  i8 
is  the  rafter  plan  of  a  house  1 8  by  24  feet;  the  rafters  are 
laid  off  on  the  level,  and  measure  nine  feet  from  centre  of 
ridge  to  outside  of  wall ;  there  should  be  a  rafter  pattern 
with  a  plumb  cut  at  one  end,  and  the  foot  cut  at  the  other, 
got  out  as  previously  shown.  (Figs.  16,  17,  18,  P.)  When  the 
rafter  foot  is  marked,  place  the  end  of  the  long  blade  of  the 
square  to  the  wall  line,  as  in  drawing,  and  mark  across  the 
rafter  at  the  outside  of  the  short  blade,  and  these  marks  on 
the  rafter  pitch  will  correspond  with  two  feet  on  the  level 
plan ;  slide  the  square  up  the  rafter  and  place  the  end  of  the 
long  blade  to  the  mark  last  made,  and  mark  outside  the  short 
blade  as  before,  repeat  the  application  until  nine  feet  are 
measured  off,  and  then  the  length  of  the  rafter  is  correct ; 
remember  to  mark  off  one-half  the  thickness  of  ridge-piece. 
The  rafters  are  laid  off  on  part  of  plan  to  show  the  appearance 
of  the  rafters  in  a  roof  of  this  kind,  but  for  working  purposes 
the  rafters  i,  2,  3,  4,  5,  and  6,  with  one  hip  rafter,  is  all 
that  is  required. 

Hip-roof  Framing. — We  first  lay  ofif  common  rafter, 
Avhich  has  been  previously  explained  ;  but  deeming  it  ne- 
cessary to  give  a  formula  in  figures  to  avoid  making  a  plan, 
we  take  yi  pitch.  This  pitch  is  ^  3  the  width  of  building,  to 
point  of  rafter  from  wall  plate  or  base.  For  an  example, 
always  use  8,  which  is  y^  of  24,  on  tongues  for  altitude;  12, 
^  the  width  of  24,  on  blade  for  base.  This  cuts  common 
rafter.     Next  is  the  hip-rafter.     It  must  be  understood  that 


36  THE     STEEL    SQUARE 

the  diagonal  of  12  and  12  is  17  in  framing,  anvi  the  hip  is 
the  diagonal  of  a  stjuare  added  to  the  rise  of  roof;  there- 
fore we  take  8  on  tongue  and  17  on  blade;  run  the  same 
number  of  times  as  common  rafter  (rule  to  find  distance 
of  hip  diagonal  a-  +  a'^  +  b'^  =  y')-  To  cut  jack  rafters,  divide 
the  numbers  of  openings  for  common  rafter.  Suppose  we 
have  5  jacks,  with  six  openings,  our  common  rafter  12  feet 
long,  each  jack  would  be  2  feet  shorter.  First  10  feet, 
second  8  feet,  third  6  feet,  and  so  on.  The  top  down  cut 
the  same  as  cut  of  common  rafter ;  foot  also  the  same. 
To  cut  mitre  to  fit  hip.  Take  half  the  width  of  building 
on  tongue  and  length  of  common  rafter  on  blade ;  blade 
gives  cut.  Now  find  the  diagonal  of  8  and  12,  which 
is  14*^,  call  it  14  7-16,  take  12  on  tongue,  14  7-16  on 
blade;  blade  gives  cut.  The  hip-rafter  must  be  beveled  to 
suit  jacks;  height  of  hip  on  tongue,  length  of  hip  on  blade; 
tongue  gives  bevel.  Then  we  take  8  on  tongue  18^  on 
blade  ;  tongue  gives  the  bevel.  Those  figures  will  span  all 
cuts  in  putting  on  cornice  and  sheathing.  To  cut  bod 
moulds  for  gable  to  fit  under  cornice,  take  half  width  of 
building  on  tongue  length  of  common  rafter  on  blade ; 
blade  gives  cut ;  machine  mouldings  will  not  member,  but 
this  gives  a  solid  joint;  and  to  member  properly  it  is  neces- 
sary to  make  moulding  by  hand,  the  diagonal  plumb  cut 
differences.  I  find  a  great  many  mechanics  puzzled  to 
makes  the  cuts  for  a  valley.  To  cut  planceer,  to  run  up 
valley,  take  heighth  of  rafter  on  tongue,  length  of  rafter  on 
blade ;  tongue  gives  cut.  The  plumb  cut  takes  the  height 
of  hip-rafter  on  tongue,  length  of  hip-rafter  on  blade; 
tongue  gives  cut.  These  figures  give  the  cuts  for  ^  pitch 
only,  regardless  of  width  of  building. 


AND    ITS    USES.  37 

For  a  hopper  the  mitre  is  cut  on  the  same  principle. 
To  make  a  butt  joint,  take  the  width  of  side  on  blade,  and 
half  the  flare  on  tongue;  the  latter  gives  the  cut.  You 
will  observe  that  a  hip-roof  is  the  same  as  a  hopper  in- 
verted. The  cuts  for  the  edges  of  the  pieces  of  a  hexagonal 
hopper  are  found  this  way  :  Subtract  the  width  of  one 
piece  at  the  bottom  from  the  width  of  same  at  top,  take 
remainder  on  tongue,  depth  of  side  on  blade ;  tongue  gives 
the  cut.  The  cut  on  the  face  of  sides  :  Take  7-12  of  the 
rise  on  tongues  and  the  depth  of  side  on  blade ;  tongue 
gives  cut.  The  bevel  of  top  and  bottom  :  Take  rise  on 
blade,  run  on  tongue ;  tongue  gives  cut. 

Fig.  19  exhibits  two  methods  of  finding  the  "backing" 
of  the  angle  on  hip-rafter.  The  methods  are  as  simple  as 
any  known.  Take  the  length  of  the  rafter  on  the  blade, 
and  the  rise  on  the  short  blade  or  tongue,  place  the 
square  on  the  line  D  E,  the  plan  of  the  hip,  the  angle  is 
given  to  bevel  the  hip-rafter,  as  shown  at  F.  This  method 
gives  the  angle,  only  for  a  right-angled  plan,  where  the 
pitches  are  the  same,  and  no  other. 

The  other  method  applies  to  right,  obtuse,  and  acute 
angles,  where  the  pitches  are  the  same.  At  the  angle  d 
will  be  seen  the  line  from  the  points  k  l,  at  the  intersec- 
tion of  the  sides  of  the  angle  rafter  with  the  sides  of  the 
plan. 

With  one  point  of  the  compass  at  d,  describe  the  curve 
from  the  line  as  shown.  Tangential  to  the  curve  draw 
the  dotted  line,  cutting  a,  then  draw  a  line  parallel  to  a  b, 
the  pitch  of  the  hip.  The  pitch  or  bevel,  will  be  found 
at  G,  which  is  a  section  of  the  hip-rafter. 

This    problem    is    taken   from   "  Gould's    Carpenters' 


THE    STEEL    SQUARE 


W 


y 


AND     ITS     USES. 


39 


Guide,"   but   has   been   in   practice   among  workmen  for 
many  years. 


Fig.  20  exhibits  a  method  of  finding  the  cuts  in  a  mitre 
box,  by  placing  the  square  on  the  line  a  b  at  equal  dis- 
tances fi-om  the  heel  of  the  square,  say  ten  inches.  The 
bevel  is  shown  to  prove  the  truth  of  the  lines  by  applying 
it  to  opposite  sides  of  the  square. 


Stairs. — In  laying  out  stairs  with  the  square,  it  is  neces- 
sary to  first  determine  the  height  from  the  top  of  the  floor 
on  which  the  stairs  start  from,  to  the  floor  on  which  they 
are  to  land  ;  also  the  "  run  "  or  the  distance  of  their  hori- 
zontal stretch.  These  lengths  being  obtained,  the  rest  is 
easy. 

Fig.  21  shows  a  part  of  a  stair  string,  with  the  "  square  " 
laid  on,  showing  its  application  in  cutting  out  a  pitch-board. 
As  the  square  is  placed  it  shows  10  inches  for  the  tread  and 
7  inches  for  the  rise. 

To  cut  a  pitch-board,  after  the  tread  and  rise  have  been 


40 


THE    STEEL    SQUARE 


determined,  proceed  as  follows :  Take  a  piece  of  thin,  clear 
stuff,  and  lay  the  square  on  the  face  edge,  as  shown  in  the 
figure,  and  mark  out  the  pitch-board  with  a  sharp  knife; 


Fig.  21. 


then  cut  out  with  a  fine  saw  and  dress  to  knife  marks,  nail 
a  piece  on  the  longest  edge  of  the  pitch-board  for  a  fence, 
and  it  is  ready  for  use. 

Fig.  2  2  is  a  rod,  with  the  number  and  heighth  of  steps 
for  a  rough  flight  of  stairs  to  lead  down  into  a  cellar  or 
elsewhere. 

Fig.  23  is  a  step-ladder,  sufficiently  inclined  to  permit  a 
person  to  pass  up  and  down  on  it  with  convenience.  To 
lay  off  the  treads,  level  across  the  pitch  of  the  ladder,  set 
the  short  side  of  the  square  on  the  floor,  at  the  foot  of  the 
string,  after  the  string  is  cut,  to  fit  the  floor  and  trimmer 
joists.  Fasten  the  fence  on  the  square,  as  shown  at  Fig.  5. 
The  height  of  the  steps  in  this  case  is  nine  inches,  so  it  will 
be  seen  that  it  is  an  easy  matter  to  lay  off  the  string,  as  the 


AND    ITS    USES. 


TOP  OF  JOIST 
5-0" 


doisr 


42  THE    STEEL   SQUARE 

long  side  of  the  square  hangs  plumb,  and  nine  inches  up 
its  length  will  be  the  distance  from  one  step  to  the  next 
one. 

Fig.  24  shows  the  square  and  fence  in  position  on  the 
string. 

The  opening  in  the  floor  at  the  top  of  the  string  shows 
the  ends  of  trimming  joists,  five  feet  apart. 

Fig.  25  shows  how  to  divide  a  board  into  an  even  number 
of  parts,  each  part  being  equal,  when  the  same  is  an  un- 
even number  of  inches,  or  parts  of  an  inch  in  width.  Lay 
the  square  as  shown,  with  the  ends  of  the  square  on  the 
edges  of  the  board,  then  the  points  of  division  will  be 
found  at  6,  12,  and  18,  for  dividing  the  board  in  four 
equal  parts;  or  at  4,  8,  12,  16,  and  20,  if  it  is  desired  to 
divide  the  board  into  six  equal  parts.  Of  course,  the 
common  two-foot  rule  will  answer  this  purpose  as  well 
as  the  square,  but  it  is  not  always  convenient. 

Fig.  26  shows  how  a  circle  can  be  described  by  means 
of  a  "  steel  square  "  without  having  recourse  to  its  centre. 

At  the  extremities  of  the  diameter,  a,  o,  fix  two  pins,  as 
shown ;  then  by  sliding  the  sides  of  the  square  in  contact 
with  the  pins,  and  holding  a  pencil  at  the  point  x,  a  semi- 
circle will  be  struck.  Reverse  the  square,  repeat  the  pro- 
cess, and  the  circle  is  complete. 

Miscellaneous  Rules  — The  following  rules  have  been 
tested  over  and  over  again  by  the  writer,  and  found  reliable 
in  every  instance.  They  have  been  known  to  advanced 
workmen  for  many  years,  but  were  never  published,  so  far 
as  the  writer  knows,  until  they  appeared  in  the  Builder  and 
Wood-  Worker,  some  years  ago : 


AND    ITS    USES.  -43 

Measurement. — Let  us  suppose  that  we  have  a  pile  of 
lumber  to  measure,  the  boards  being  of  different  widths,  and 
say  1 6  feet  long.  We  take  our  square  and  a  bevel  with  a 
long  blade  and  proceed  as  follows  :  First  we  set  the  bevel 
at  1 2  inches  on  the  tongue  of  the  square,  because  we  want 
to  find  the  contents  of  the  board  in  feet,  12  inches  being 
one  foot ;  now  we  set  the  other  end  of  the  bevel  blade  on  the 
16  inch  mark  on  the  blade  of  the  square,  because  the  boards 
are  16  feet  long.  Now,  it  must  be  quite  evident  to  any- 
one who  would  thmk  for  a  moment,  that  a  board  1 2  inches, 
or  one  foot  wide,  and  16  feet  long,  must  contain  16  feet  of 
lumber.  Very  well,  then  we  have  16,  the  length,  on  the 
blade.  Now,  we  have  a  board  11  inches  wide,  we  just 
move  our  bevel  from  the  1 2  inch  mark  to  the  1 1  inch  mark, 
and  look  on  the  blade  of  the  square  for  the  true  answer ; 
and  so  on  with  any  width,  so  long  as  the  stuff  is  16  feet 
long.  If  the  stuff  is  2  inches  thick,  double  the  answer,  if 
3  inches  thick,  treble  the  answer,  etc. 

Nov/,  if  we  have  stuff  14  kec  iong,  we  simply  change 
the  bevel  blade  from  16  inches  on  the  square  blade,  to  14 
inches,  keeping  the  other  end  of  the  bevel  on  the  1 2  inch 
mark,  12  inches  being  the  constant  figure  on  that  side  of 
the  square,  and  it  will  easily  be  seen  that  any  length  of 
stuff  within  the  range  of  the  square  can  be  measured  ac- 
curately by  this  method. 

If  we  want  to  find  out  how  many  yards  of  plastering  or 
painting  there  are  in  a  wall,  it  can  be  done  by  this  method 
quite  easily.  Let  us  suppose  a  wall  to  be  12  feet  high  and 
18  feet  long,  and  we  want  to  find  out  how  many  yards  of 
plastering  or  painting  there  are  in  it,  we  set  the  bevel  on 
the  9  inch  mark  on  the  tongue  (we  take  9  inches  because  9 


44  I'HE    STEEL   SQUARE 

square  feet  make  one  square  yard,)  we  take  i8  inches,  one 
of  the  dimensions  of  the  wall,  on  the  blade  of  the  square ; 
then  after  screwing  the  bevel  tight,  we  slide  it  from  9  inches 
to  12  inches,  the  latter  number  being  the  other  dimension, 
and  the  answer  will  be  found  on  the  blade  of  the  square. 
It  must  be  understood  that  9  inches  must  be  a  constant 
figure  when  you  want  the  answer  to  be  in  yards,  and  in 
measuring  for  plastering  it  is  as  well  to  set  the  other  end  of 
the  bevel  on  the  figure  that  corresponds  with  the  height  of 
the  ceiling,  and  then  there  will  require  no  movement  of 
the  bevel  further  than  to  place  it  on  the  third  dimension. 
This  last  rule  is  a  very  simple  and  very  useful  one ;  of  course 
"  openings  "  will  have  to  be  allowed  for,  as  this  rule  gives 
the  whole  measurement. 

If  the  diagonal  of  any  parallelogram  within  the  range  of 
the  square  is  required,  it  can  be  obtained  as  follows :  Set  the 
blade  of  the  bevel  on  83^  in.  on  the  tongue  of  the  square, 
and  at  12^  in.  on  the  blade ;  securely  fasten  the  bevel  at  this 
angle.  Now,  suppose  the  parallelogram  or  square  to  be  11 
inches  on  the  side,  then  move  the  bevel  to  the  1 1  inch  mark 
on  the  tongue  of  the  square,  and  the  answer,  15  9-16,  will  be 
found  on  the  blade.  All  problems  of  this  nature  can  be  solved 
with  the  square  and  bevel  as  the  latter  is  now  set.  There 
is  no  particular  reason  for  using  8^  and  12^,  only  that 
they  are  in  exact  proportion  to  70  and  99.  4^  and  6 
3-16  would  do  just  as  well,  but  would  rot  admit  as  ready 
an  adjustment  of  the  bevel. 

To  find  the  circumference  of  a  circle  with  the  square  and 
bevel  proceed  as  follows :  Set  the  bevel  to  7  on  the  tongue 
and  22  on  the  blade;  move  the  bevel  to  the  given  diameter 
on  the  tongue  of  the  square,  and  the  approximate  answer 


AND     ITS     USES.  45 

Mrill  be  found  on  the  blade.  When  the  circumference  is 
wanted  the  operation  is  simply  reversed,  that  is,  we  put 
the  bevel  on  the  blade  and  look  on  the  tongue  of  the  square 
for  the  answer. 

If  we  want  to  find  the  side  of  the  greatest  square  that 
can  be  inscribed  in  a  given  circle,  when  the  diameter  is 
given,  we  set  the  bevel  to  S^^  on  the  tongue  and  12  on  the 
blade.  Then  set  the  bevel  of  the  diameter,  on  the  blade, 
and  the  answer  will  be  found  on  the  tongue. 

The  circumference  of  an  ellipse  or  oval  is  found  by  set- 
ting 5^'^  inches  on  the  tongue  and  83/(  inches  on  the  blade; 
then  set  the  bevel  to  the  sum  of  the  longest  and  shortest 
diameters  on  the  tongue,  and  the  blade  gives  the  answer. 

To  find  a  square  of  equal  area  to  a  given  circle,  we  set  the 
bevel  to  9^  mches  on  the  tongue,  and  1 1  inches  on  the  blade; 
then  move  the  bevel  to  the  diameter  of  the  circle  on  the 
blade,  and  the  answer  will  be  found  on  the  tongue.  If  the 
circumference  of  the  circle  is  given,  and  we  want  to  find  a 
square  containing  the  same  area,  we  set  the  bevel  to  5j/^ 
inches  on  the  tongue  and  1914  inches  on  the  blade. 

On  Fig.  27  is  shown  a  method  to  determine  the  pro- 
portions of  any  circular  presses  or  other  cylinderical  bodies, 
by  the  use  of  the  square.  Suppose  the  small  circle,  n,  to 
be  five  inches  in  diameter  and  the  circle  r  is  ten  inches  in 
diameter,  and  it  is  required  to  make  another  circle,  z,  to 
contain  the  same  area  as  the  two  circles  n  and  r.  Meas- 
ure line  a.,  on  the  square  d,  from  five  on  the  tongue  to  10 
on  the  blade,  and  the  length  of  this  line  a  from  the  two 
points  named  will  be  the  diameter  of  the  larger  circle  z. 
And  again,  if  you  want  to  run  these  circles  into  a  fourth 
one,  set  the  diameter  of  the  third  on  the  tongue  of  the  square, 


46 


THE     STEEL    SQUARE 


and  the  diameter  of  z  on  the  blade,  and  the  diagonal 
will  give  the  diameter  of  the  fourth  or  largest  circle,  and  the 
same  rule  may  be  carried  out  to  infinite  extent.  The  rule 
is  reversed  by  taking  the  diameter  of  the  greater  circle  and 
laying  diagonally  on  the  square,  and  letting  the  ends  touch 

0  .         


prrrTTTnTn 


Fig.  27. 


vhatever  points  on  the  outside  edge  of  the  square.  These 
points  will  give  the  diameter  of  two  circles,  which  com- 
bined, will  contain  the  same  area  as  the  larger  circle.  The 
same  rule  can  also  be  applied  to  squares,  cubes,  triangles, 
rectangles,  and  all  other  regular  figures,  by  taking  similar 
dimensions  only;  that  is,  if  the  largest  side  of  one  triangle 
is  taken,  the  largest  side  of  the  other  must  also  be  taken, 
and  the  result  will  be  the  largest  side  of  the  required  tri- 
angle, and  so  with  the  shortest  side. 

In  Fig.  28  we  show  how  the  centre  of  a  circle  may  be  de- 
termined without  the  use  of  compasses;  this  is  based  on 
the  principle  that  a  circle  can  be  drawn  through  any  three 
points  that  are  not  actually  in  a  straight  line.  Suppose  we 
take  A  B  c  D  for  four  given  points,  then  draw  a  line  from  a 


AND    ITS    USES. 


47 


to  D,  and  from  b  to  c ;  get  the  centre  of  these  Hnes,  and 
square  from  these  centres  as  shown,  and  when  the  square 
crosses,  the  Hne,  or  where  the  hnes  intersect,  as  at  x,  there 
will  be  the  centre  of  the  circle.  This  is  a  very  useful  rule,  and 


Fig.  28. 


by  keeping  it  in  mind  the  mechanic  may  very  frequently 
save  himself  much  trouble,  as  it  often  happens  that  it  is  ne- 
cessary to  find  the  centre  of  the  circle,  when  the  compasses 
are  not  at  hand. 

In  Fig.  29  we  show  how  the  square  can  be  used,  in  lieu 
of  the  trammel,  for  the  production  of  eUipses.  Here  the 
square,  E  d  f,  is  used  to  form  the  elliptical  quadrant, 
A  B,  instead  of  the  cross  of  the  trammel ;  h  I  k  may  be 
simply  pins,  which  can  be  pressed  against  the  sides  of  the 
square  while  the  tracer  is  moved.  In  this  case  the  adjust- 
ment is  obtained  by  making  the  distance,  h  /,  equal  to  the 
semi-axis  minor,  and  the  distance  /  k,  equal  to  the  semi-axis 
major. 


48 


THE     STEEL    SQUARE 


Fig.  29. 


Fig.  30  shows  a  method  of  describing  a  parabola  by 
means  of  a  straight  rule  and  a  square,  its  double  ordinate 
and  abscissa  being  given.  Let  a  c  be  the  double  ordinate, 
and  D  B  the  abscissa.  Bisect  DC  in  f  ;  join  b  f,  and  draw 
F  E  perpendicular  to  b  f,  cutting  the  axis  b  d  produced  in 
F  From  B  set  off  b  g  equal  to  D  E,  and  G  will  be  the  focus 
of  the  parabola.  Make  b  l  equal  to  b  g,  and  lay  the  rule 
on  straight-edge  h  k  on  l,  and  parallel  to  a  c.  Take  a 
string,  M  F  G,  equal  in  length  to  l  E ;  attach  one  of  its  ends 
to  a  pin,  or  other  fastening,  at  G,  and  its  other  end  to  the 
end  M,  of  the  square  M  n  o.  If  now  the  square  be  slid 
along  the  straight-edge,  and  the  string  be  pressed  against 


AND    ITS    USES. 


49 


its  edge  m  n,  a  pencil  placed  in  the  bight  at  f  will  describe 
the  curve. 


The  two  arms  of  a  horizontal  lever  are  respectively 
9  inches  and  13  inches  in  length  from  the  suspending 
point;  a  weight  of  10  lbs.  is  suspended  from  the  shorter 
arm,  and  it  is  required  to  know  what  weight  will  be  re- 
quired to  suspend  on  the  long  arm  to  make  it  balance. 
Set  a  bevel  on  the  blade  of  square  at  13  inches  and  the 
other  end  of  the  bevel  on  the  9  inch  mark  on  tongue  of 
square,  then  shde  the  bevel  from  13  inches  to  10  on  the 
blade  of  square,  and  the  answer  will  be  found  on  the 
tongue  of  the  square.  It  is  easy  to  see  how  this  rule  can 
be  reversed  so  that  a  weight  required  for  the  shorter  arm 
can  be  found. 

Fig.  31  shows  how  to  get  the  tlare  for  a  hopper  4  feet 
across  the  top  and  16  inches  perpendicular  depth.  Add  to 
the  depth  one-third  of  the  required  size  of  the  discharge 


so 


THE    STEEL    SQUARE 

HfiLFOFDISCHfiPCe^  H"^ 


(.. 2^0^: 

HALF  WIDTH  OF  HOPPER  TOP 
Fig.  31. 


hole  (the  draft  represents  a  6-inch  hole),  which  makes  18 
inches,  which  is  represented  on  the  tongue  of  the  square. 
(The  figures  on  the  draft  are  9  and  12,  which  produce  the 
same  bevel.)  Then  take  one-half,  24  inches  of  the  width 
across  the  top  of  the  hopper,  which  is  represented  on  the 
blade  of  the  square.  Than  scribe  along  the  blade  as  rep- 
resented by  the  dotted  lines,  which  gives  the  required  flare. 
(The  one-third  added  to  the  depth  is  near  enough  for 
all  practical  purpose  for  the  discharge.) 


Fig.  32. 


AND    ITS    USES. 


s* 


Fig.  32  shows  how  to  apply  the  square  to  the  edge  of 
a  board  in  order  to  obtain  the  bevel  to  form  the  joint. 
Using  the  same  figures  as  in  Fig.  31,  scribe  across  the  edge 
of  the  board  by  the  side  of  the  tongue,  as  shown  by  dotted 
lines.     The  long  point  being  the  outside. 


^N     \ 


Fig.  33. 


On  Fig.  33  we  show  a  quick  method  of  finding  the 
centre  of  a  circle:  Let  N  n,  the  corner  of  the  square,  touch 
the  circumference,  and  where  the  blade  and  tongue  cross 
it  will  be  divided  equally ;  then  move  the  square  to  any 
other  place  and  mark  in  the  same  way  and  straight  edge 
across,  and  where  the  line  crosses  a,  b,  as  at  o,  there  will 
be  the  centre  of  the  circle. 


52 


THE     STEEL    SQUAkE 


lines  for  eight-sciuaring 


I  and  2,  Fig.  34,  are  taken  from  Gould's    Wood- Work- 
ing Guide. 

The  portion  marked  a,  exhibits  a  method  of  finding  the 
a  piece  of  timber  with  the  square, 
by  placing  the  block  on  the 
piece,  and  making  the  points 
seven  inches  from  the  ends 
of  the  square,  from  which  to 
draw  the  lines  for  the  sides 
of  the  octagonal  piece  re- 
quired. 

At  the  heel  of  the  square 
is   shown   a  method  of  cut- 
ting a  board  to  fit  any  angle 
^    with  the  square  and  compass, 
o    by  placing  the  square  in  the 
^    angle,  and  taking  the  distance 
from  the  heel  of  the  square 
to  the  angle  a,  in  the  com- 
pass ;  then  lay  the  square  on 
the  piece  to  be  fitted,  with 
the  distance  taken,  and  from 
the  point  a,  draw  the  line  a 
B,  which  will  give  the  angle 
to  cut  the  piece  required. 

At  2  is  shown  a  method 
of  constructing  a  polygonal 
figure  of  eight  sides ;  by  placing  the  square  on  the  line  a  b, 
with  equal  distances  on  the  blade  and  tongue,  as  shown ; 
the  curve  lines  show  the  method  of  transferring  the  di? 
tances;  the  diagonal  gives  the  intersection  at  the  angles. 


"*^ 

1 

-^ 

w 

i 

1 

1 

1 

'k 

m 

m 

!.:r 

'$(! 

111 

J 

i 

Ik 

M 

AND   ITS    USES. 


53 


There  are  at  least  a  dozen  different  ways  of  forming  oc- 
tagonal figures  by  the  square ;  some  of  them  are  tedious 
and  difficult,  while  others  can  not  be  applied  under  all  cir- 
cumstances. The  method  shown  at  Fig.  35  is  handy  and 
easily  understood. 


Fig.  35. 

An  equilateral  triangle  can  be  formed  by  taking  half  of 
one  side  on  the  tongue  of  the  square,  as  shown  at  Fig.  36. 
The  line  along  the  edge  of  the  tongue  forms  the  mitre  fbr 


Fig.  36. 


the  triangle,  and  the  line  along  the  edge  of  the  blade  forms 
the  mitre  cut  for  the  joviits  of  a  hexagon,  and  as  six  equi- 


54 


THE    STEEL    SQUARE 


lateral  triangles  form  a  hexagon  when  one  point  of  each  is 
placed  at  a  central  point,  o,  it  follows  that  a  hexagon  may 
be  constructed  by  the  square  above. 

The  following  is  a  good  method  for  obtaining  the  cuts 
for  a  horizontal  and  raking  cornice ;  it  is  correct  and  simple ; 
the  gutter  to  be  always  cut  a  square  mitre. 

The  seat  or  run  of  the  rafter  on  the  blade,  r  c,  Fig,  37, 
the  rise  of  the  roof  on  the  tongue,  A  c,  mark  against  the 
tongue,  gives  the  cut  for  the  side  of  the  box,  a  c.     The 


Fig.  37- 

diagonal  a,  r,  which  is  the  length  of  the  rafter  on  the  blade 
a,  d,  the  seat  of  the  rafter  on  the  tongue  d,  s,  mark  against 
the  blade  gives  the  cut  across  the  box,  ad.  d  a  c  is  the 
mitre  cut  to  fit  the  gutter;  then  if  we  square  across  the 
box  from  a,  it  gives  f,  a,  c  the  cut  for  the  gable  peak. 

At  Fig.  38  is  shown  a  method  for  obtaining  either  the 
butt  or  mitre  cuts,  for  "  Hopper"  work. 

The  line,  s  s,  in  the  cut  represents  the  edge  of  a  board ; 
the  line,  a  b,  the  flare  of  hopper.  Lay  the  square  on  the 
face  of  the  board  so  that  the  blade  will  coincide  with  flare 
of  hopper,  a  b,  tlien  mark  by  the  tongue  the  line  b  c,  tlien 
square  from  edge  of  board,  s  s,  cutting  the  angle  B. 

Now  we  have  a  figure  that  will,  when  used  on  the  steei 


AND    ITS    USES. 


55 


square,  give   the  cuts  for  a  hopper  of  any  flare,  eitlier  with 

butt  or  mitre  joints. 

To  find  bevel  to  cut  across  face  of  board : 

Take  a  b  on  blade  and  A  d  on  tongue,  bevel  of  tongue 

is  the  bevel  required. 


Fig   38. 

To  find  the  bevel  for  butt-joint :  Take  b  c  on  blade 
and  A  D  on  tongue ;  bevel  of  tongue  is  the  bevel  required. 

To  find  the  bevel  for  mitre  joint :  Take  b  c  on  blade 
and  D  c  on  tongue;  bevel  of  tongue  is  the  bevel  required. 

It  will  be  seen  that  this  is  a  very  simple  method  of 
solving  what  is  usually  considered  a  very  difficult  problem. 


56  THF.     STKEL    bCJUAKE 


PART    II. 

The  following  useful  applications  of  the  square  were 
kindly  furnished  for  this  work,  by  Mr.  Croker;  several  of 
them  are  new  and  original : 

Consider  the  blade  of  the  square  as  representing  the 
span  of  a  building,  but  without  any  reference  to  actual  or 
scale  measurement.  Next,  some  particular  portion  of  the 
blade  is  to  be  taken  as  the  rise  of  the  supposed  building ;  if 
a  third,  fourth,  or  half  pitch  is  required,  then  a  third, 
fourth,  or  a  half  of  the  blade  is  conceived  as  the  rise  which 
with  half  the  blade  solves  the  pitch.  From  this  it  will  be 
seen  that  half  the  blade  is  always  taken  as  the  base  of  the 
theoretical  common  rafter.  Where  we  have  to  deal  with 
irregular  pitches — by  which  is  meant  those  pitches  which 
are  not  a  quarter,  sixth,  third,  half,  etc.,  of  the  building — 
then  the  square  is  to  be  applied  to  the  irregular  pitch 
with  the  blade  lying  in  the  direction  of  the  pitch  and 
the  centre  of  the  blade  at  the  intersection  of  pitch  and 
base  line  of  the  common  rafter,  and  the  resulting  distance 
on  the  tongue,  where  it  intersects  the  base  line,  is  the 
distance  to  be  taken  as  the  rise  of  the  theoretical  rafter. 
Let  us  now  take  a  hip-roof  over  a  square  plan  (for  all  the 
rules  apply  only  to  scjuare  planned  building),  and  the  prac- 
tical problems  supposed  to  need  solution  are :  Length  of 
common  rafters,  the  plumb  and  level  cuts;  length  of  hip- 
rafter,  its  plumb  and  level  cuts ;  bevel  of  jacks  and  sheet- 


AND     ITS     USES. 


57 


ing  boards  against  the  hips  ;  "  backing  "  of  the  hip-rafter, 
top  and  down  bevel  of  a  purhn  mitering  against  the  hip 
with  its  surface  in  Hne  with  the  plane  of  the  roof  If  the 
student  can  readily  and  intelligently  solve  these  problems, 
he  w'ill  be  in  a  position  to  make  extensions  in  the  principles 
involved.  Let  the  width  of  building  under  consideration 
be  24  feet  wide,  and  of  one  third  ])itch. 


Fig.  -,6. 


Let  I,  12.  Fig.  36,  be  the  base  of  the  theoretical  common 
rafter,  eight  inches  rise,  equal  to  one  third  of  the  blade,  be- 
cause it  is  a  third  pitch;  mark  along  the  blade  and  extend 
the  heel,  making  it  and  12  equal  to  half  the  width  of 
the  actual  building  to  a  scale  oi  1%  inch  to  a  foot ;  this  is  a 
much  better  scale  to  work  by  than  an  inch  one,  being  larger 
and  more  legible,  eighths  behig  inches,  sixteenths,  ^  inches, 
etc.,  thus  enabling  very  accurate  measurements  to  be  taken. 
By  the  way,  it  is  a  good  plan  to  have  the  square  stamped 
off  on  the  eighths  side  at  every  i  y^.  inches  for  feet,  for  more 
readily  counting  the  scale ;  then  mark  along  the  tongue  at 
B,  which  gives  b  12  the  length  of  common  rafter;  level  cut 
on  blade  and  plumb  cut  on  tongue.  Next  take  the  rise  of 
the  theoretical  common  rafter  on  the  tongue,  and  1 7  inches 


58 


THE    STEEL    SQUARE 


on  the  blade,  as  the  theoretical   base  of   the  hip-rafter; 
place  the  square  as  shown  at   Fig.   37  ;  then  multiply  the 


Fig.  37. 

actual  base  of  common  rafter  12,  (Fig.  36.)  by  1-414  = 
16-968  feet,  or  17  feet,  practically,  which  set  off  on  blade  at  A 
1 7  ;  mark  on  tongue  at  b,  then  b  1 7  is  the  length  of  hip- 
rafter.  For  the  bevels  of  jacks  and  sheeting-boards  against 
hips  take  the  diagonal  b  12 — theoretical  rafter — Fig,  36,  on 
the  blade  \vith  half  the  blade — the  theoretical  base — and 
place  the  square  as  shown  at  Fig.  38,  then  mark  along  the 
blade  for  bevel  of  jacks,  and  along  tongue  for  bevel  of 
sheeting-boards. 


Fig.  38, 


AND     ITS     USES. 


59 


For  the  "  backing "  of  hip,  take  the  diagonal  of  the 
theoretical  hip-rafter,  8,  17  (Fig  37),  on  the  blade,  and  its 
rise — 8  inches — on  the  tongue,  and  place  square  as  shown 
at  Fig.  39;  mark  by  the  tongue  which   gi\es  the  bevel  re- 


FlG.   39. 


quired.  To  get  the  upper  bevel  of  a  purlin  lying  in 
the  plane  of  the  roof,  take  the  beve\  at  tongue  (Fig.  38), 
for  the  down  bevel  take  the  blade  distance  147 — 16  (Fig, 
38)  on  the  blade  with  the  theoretical  rise — 8  ;  place  the 
square  as  shown  at  Fig.  40 ;  mark  by  the  tongue  which 
gives  the  bevel  required. 


Fig.  40. 


Fig.  41  shows  how  any  length  or  breadth  within  the  extent 
of  the  blade  of  the  square  can  be  instantly  divided  into  any 
equal  parts.  Let  a  and  b  represent  the  edges  of  a  board,  say 
8^  inches,  wide,  to  be  divided  into  5  equal  parts;  take  any 


6o 


THE    STEEL    SQUARE 


convenient  5  parts,  say  1 5  inches,  because  5X3  =  15,  placing 
heel  of  square  fair  to  edge  B,  and  1 5  to  edge  a  ;  mark  off  at 
every  3  inches  on  blade,  as  shown,  and  draw  lines  through 
these  points,  which  will  divide  the  board  as  required.  We 
will  here  show  how  the  square  can  be  used  to  solve  problems 
in  proportion;  for  instance,  if  1500  feet  of  boards  cost 
$10.75,  what  will  600  feet  cost?     Take  15  on  the  blade 


Fig.  41. 


and  io*75  on  the  tongue,  and  place  the  square  as  shown  at 
Fig.  41,  then  count  from  15  towards  b,  and  from  this  point 
draw  parallel  to  tongue;  6  a,  this  is  the  answer  re- 
quired. 


Fig.  42. 


Fig.  43, 


AND    ITS    USES. 


6i 


Figs.  42  and  43  show  quite  a  novel  and  useful  way  of 
bisecting  any  angle.  Let  a  i  2,  a  b  be  the  given  sides  of  an 
acute  angle  to  be  bisected.  At  any  convenient  point  as  c 
square  c  d  from  c  12.  Now  take  c  d  on  the  tongue,  and 
the  sum  of  a  d  and  a  c  on  the  blade  of  the  square,  place 
as  shown  in  the  Figure,  then  mark  by  the  blade,  which  is 
the  bisection  required.  If  the  angle  is  obtuse,  as  a  b,  a  f, 
(Fig.  42),  produce  a  convenient  distance,  as  a  c,  square 
over  c  D,  take  c  D  on  the  tongue,  and  the  sum  of  a  d,  a  c, 
on  the  blade,  place  square  as  shown,  and  mark  by  the 
tongue  for  the  required  bisection. 


Fig.  44  shows  a  handy  way  of  finding  the  bevel  of  rails 
to  diminish  door  stiles.  Place  the  square  fair  with  the 
known  joint  a  b,  mark  by  the  tongue,  then  the  resulting 
bevel  at  a  is  the  same  as  that  at  B. 


62 


THE    STEEL    SQUARE 


PART  III. 

The  following  rules  have  been  gathered  from  various 
sources,  chiefly,  however,  from  papers  recently  published  in 
the  Scientific  American  Supplement,  by  John  O.  Connell,  of 
St.  Louis,  and  from  papers  contributed  to  the  Builder  and 
Wood-Wo? ker,  by  Wm.  E.  Hill,  of  Terre  Haute,  Ind. 


Fig.  45 


*  Fig.  45  shows  how  an  octagon  can  be  produced  by  the 
aid  of  a  steel  square.  Prick  off  the  distance  a  o  equal  to 
half  the  distance  of  the  square ;  mark  this  distance  on  the 
blade  of  the  square  from  b  to  o,  place  the  square  on  the 

*  Wm.  E.  HilL 


AND    ITS    USES. 


63 


diagonal,  as  shown,  and 
square  over  each  way.  Do 
the  same  at  ever)'  angle, 
and  the  octagon  is  com- 
plete. 

To  obtain  the  same  figure 
with  the  compasses,  pro- 
ceed as  follows  :  Take  half 
the  diagonal  on  the  com- 
passes, make  a  little  over  a 
quarter  sweep  from  c,  and 
at  the  insersection  at  d  and 
c,  then  D  and  c  form  one 
side  of  an  octagonal  figure. 

Again:  take  a  piece  of 
timber  twelve  inches  square, 
as  at  Fig.  46  ;  take  twelve 
inches  on  the  blade  and 
tongue  from  a  to  b,  and  a 
to  c,  mark  at  the  point  a, 
operate  similarly  on  the  op- 
posite edge,  and  the  marked 
points  will  be  guides  for 
guage-lines  for  the  angles 
forming  an  octagon.  The 
remaining  three  sides  of  the 
timber  can  be  treated  in 
the  same  manner. 

These  points  can  be 
found  with  a  carpenter's 
rule  as  follows:     Lay   the 


64 


THE    STEEL    SQUARE 


rule  on  the  timber,  partly  opened,  as  shown,  in  the  cut, 
"prick  off"  at  the  figures  7  and  17  as  at  a  and  B,  and 
these  points  will  be  the  guides  for  the  gauge-lines.  The 
same  points  can  be  found  by  laying  the  square  diagonally 
across  the  timber  and  '•  pricking  "  off  7  and  17. 

To  make  a  moulder's  flask  octagonal  proceed  as  follows : 
The  flask  to  be  four  feet  across.  Multiply  4  X  5  (as  an 
octagon  is  always  as  5  to  12  nearly),  which  gives  20;  di- 
vide by  12,  which  gives  12,^  feet,  cut  mitre  to  suit  this 
measurement,  nail  into  corners  of  square  box,  and  you  have 
an  octagon  flask  at  once. 

Another  method  of  constructing  an  octagon  is  shown  at 
Fig.  47.     Take  the  side  as  a  ^  for  a  radius,  describe  an  arc 


Fig.  47. 


cutting  the  diagonal  at  d\   square  over  from  d  to  e,  and 
the  point  e  will  then  be  the  gauge-guide  for  all  the  sides. 


AND     ITS     USES. 


6S 


Another  method  (Fig.  48)  is  to  draw  a  straight  hne,  c 
b,  any  length;  then  let  a  b  and  a  c  ho.  corresponding 
figures  on  the  blade  and  tongue  of  the  square,  mark  along 
either  and  measure  the  distance  of  required  octagon ;  move 


Fig.  48. 


the  square  and  mark  also.  Now  use  the  square  tho 
same  as  before,  and  the  marks  c  b  and  b  d  are  the  poin  ,s 
required. 

Fig.  49  shows  the  application  of  a  long  bevel  to  a 
square,  by  which  some  calculations  can  be  made  with 
greater  ease  and  quickness  than  by  the  usual  arithmetical 
process.  The  largest  size  of  carpenter's  bevel  placed  under 
the  framing  square  will  answer  in  nearly  every  case.  One 
edge  of  each  blade  should  be  perfectly  straight  and  the 
edge  of  L  should  be  cut  out  in  several  places  to  see  the 
blade  E,  when  placed  under  the  square.  The  two  blades 
ghould  be  fastened  together  by   a  thumb-screw,     Ther§ 


66 


THE     STEEL    SQUARE 


should  be  three  holes  in  l,  one  near  each  end  and  one  in 
the  middle,  and  a  notch  filed  by  each  hole,  so  that  the 
blade  e,  may  be  shifted  when  necessary. 


Fig,  49 

*To  Find  the  Diagonal  of  a  Square  by  this  instrument,  set 
the  blade  e  to  8^  inches  on  the  tongue  and  12^  inches 
on  the  blade.  Then  screw  the  bevel  fast ;  and  supposing 
the  side  of  the  square  in  question  is  1 1  inches,  move  blade 
E  to  the  II  inch  mark  on  the  tongue,  keeping  blade  L 
against  the  square,  when  blade  e  will  touch  15  9-16  inches 
on  the  blade,  which  is  the  required  diagonal.  There  is  no 
special  reason  for  using  8^  and  12^  ;  other  numbers  may 
be  employed  provided  the  proportion  of  70  to  99  exists 
between  them.  In  the  problem  just  solved  as  in  all  that 
follcw,  the  bevel  being  once  set  to  solve  a  particular  ques- 

"J.  O.  ConnelU 


AND     ITS     USES. 


67 


tion  will  solve  all  the  others  of  the  same  kind,  till  the  bevel 
is  altered. 

Polygons  Inscribed  In  Circles. — In  the  following  table,  set 
the  bevel  to  the  pair  of  numbers  under  the  polygon  to  be 
inscribed. 

No.  of  sides.            345                6  7  89  10  11  12 

Radius 56         70        74            Side  60  98         22  89  80  85 

Side 97        99         87        equal  to  52  75         15  55  45  44 

radius. 

If  we  require  the  radius  of  a  circle  which  will  circum- 
scribe an  octagon  8  inches  on  a  side,  we  refer  to  column  8, 
take  98  parts  on  the  blade  and  76  on  tongue,  and 
tighten  the  bevel.  As  the  side  of  a  hexagon  equals  the 
radius  of  its  circle,  the  side  of  an  octagon  must  be  less  than 
the  radius ;  hence  we  shift  to  8  inches,  that  end  of  the  bevel 
blade  which  gives  the  lesser  number,  in  this  case,  on  the 
tongue  of  the  square,  as  the  75  parts  to  which  the  bevel 
was  set  are  less  than  the  98.  The  required  radius  is  then 
indicated  on  the  blade. 

We  will  now  explain  the  figures  used  in  stepping  round 
a  circle  forming  inscribed  polygons  from  three  to  twelve 
sides  :  Set  bevel  or  fence  to  1 2  on  blade,  and  the  number 
opposite  each  polygon  on  tongue ;  move  to  diameter  of 
circle ;  answer  of  the  side  of  polygon  on  tongue. 

Names.  No.  of  Sides,  Gauge  Points. 

Triangle 3  1040 

Square 4  8  '49 

Pentagon 5  7"o5 

Hexagon 6  6  00 

Heptagon 7  521 

Octagon 8  4'6o 

1^  onagon 9  411 

Decagon id  3"7i 

Undecagon 11  3'3g 

Dodecagon ^ 12  j'li 


68  THE    STEEL    SQUARE 

To  divide  a  circle  into  a  given  number  of  parts,  multiply  ' 
the  corresponding  number  in  column  one  and  the  product 
is  the  chord  to  lay  off  on  circumference.  The  side  of  a 
polygon  is  known,  to  find  the  radius  of  a  circle  that  will 
circumscribe  :  Multiply  the  given  side  by  the  correspond- 
ing number  opposite  of  polygon  in  column  two. 

No.  rf  A  ngle  of 

Sides.           Name  of  Polygon.         Angle.  Polygon.  Cobanm.  Column  2. 

3  Triangle 12O  60  '732  '5773 

4  Square 90  90  ''414  '7071 

5  Pentagon 72  108  1 '773  '8510 

6  Hexagon 60  120  Radius.  Side. 

7  Heptagon SJ  3-7  1284-7  -8677  1152 

8  Octagon 45  135  7653  t'so?' 

9  Nonagon 40  140  6840  i'4863 

10  Decagon   36  144  '6180  i'6i8i 

11  Undecagon 328-11  147  3-1 1  '5634  i"7754 

12  Dodecagon 30  150  '5176  i'9323 

The  side  of  a  polygon  is  known,  to  find  the  length  of 
perpendicular :  Set  bevel  or  fence  to  the  tabulated  numbers 
below.  Example  :  The  side  of  an  octagon  is  1 2,  set  bevel 
to  23  on  tongue,  27  11-16  on  blade.  Blade  gives  the 
answer. 

No.  0/  Sides.       3  45  67  8  9  10  11  12 

Perpendicular.,     g  13°  '3      273-4     277-10    503-4     281-2     .-13-4     26 

Sidcof  Polygon  31  1-5     2     351-4     i5     26  23  37  18  1-2     301-2     14 

To  Inscribe  three  Equal  Circles  in  a  circle  of  given  diame- 
ter. Set  to  6)4  on  tongue  and  14  on  blade.  Move  the  bevel 
to  the  given  diameter  on  the  blade  and  the  required 
diameter  appears  on  the  tongue. 

Four  equal  circles  require  a  bevel  of  2-91  and  14. 

The  following  also,  is  another  use  for  the  square  aijd 
bevel  combined. 

If  a  person  is  drawing  a  machine  on  a  scale  of  i^  inch 
to  the  foot,  he  may  simply  lay  a  common  rule  under  tJiQ 


AND     ITS     USES. 


69 


square,  touching  the  12  inch  mark  on  the  blade,  and  the 
i^  inch  mark  on  the  tongue;  he  then  possesses  a  con- 
trivance by  which  he  may  easily  reduce  from  one  scale  to 
the  other.  For  instance,  if  a  piece  of  stick  2^  inches 
square  is  to  go  into  the  construction,  the  draughtsman  finds 
the  g}(  inch  mark  on  the  blade,  that  is  2^  inches  back 
from  the  12  inch  mark,  and  measures  square  out  to  the 
rule.  This  distance  is  the  reduced  section  of 'the  stick. 
A  straight  mark,  drawn  on  a  table  or  a  drawing  board, 
serves  as  well  as  a  rule. 

Conveyors'  sh^ft  5  inches  in  diameter,  1 2  feet  long,  pitch 
of  flights  9  inches ;  make  a  posteboard  template ;  multiply- 
ing the  diameter  by  yi4i6  gives  the  base,  and  the  9  is  the 
altitude.  The  paper  would  be  9  inches  altitude,  15  71-100 
base ;  draw  a  line  along  shaft,  place  altitude  or  9  inches  along 
this  line,  scribe  along  the  hypothenuse ;  this  gives  the  spiral 
course  of  flight.  This  principle  also  teaches  how  to  cut  round 
sticks  of  straight  timber  by  marking  along  base  of  template, 
take  square  on  each  end  the  same  as  taking  a  stick  out  of 
wind,  before  striking  lines. 

The  cuts  for  the  edges  of  the  pieces  of  a  hexagonal  hop- 
per are  found  by  subtracting  the  width  of  one  piece  at  the 
bottom,  viz.,  the  width  of  same  at  top,  and  taking  the  re- 
mainder on  the  tongue,  and  depth  of  side  on  blade.  The 
tongue  gives  the  cut.  For  the  cut  on  the  face  of  the  sides, 
take  7-12  of  the  rise  on  the  tongue,  and  the  depth  of  side 
on  the  blade.  The  tongue  gives  the  cut.  The  bevel  for 
the  top  and  bottom  edges  is  found  by  taking  the  rise  on 
the  blade,  and  the  run  on  the  tongue ;  the  latter  gives  the 
cut. 

To  find  the  cut  of  an  octagonal  hopper  for  the  face  of 


yd  THE    STEEL    SQUARE 

the  board  and  also  the  edge,  substract  the  rise  from  the 
width  of  side;  take  the  remainder  on  the  tongue  and  width 
of  side  on  blade;  the  tongue  gives  the  cut.  The  edge  of 
the  stuff  is  to  be  square  when  applying  the  bevel.  The 
bevel  for  the  top  and  bottom  edges  of  the  sides  is  found  by- 
taking  the  rise  on  the  blade,  and  run  on  the  tongue,  the 
latter  gives  the  cut.  This  makes  the  edges  horizonatal. 
The  edges  are  not  to  be  beveled  till  the  four  sides  are 
cut. 

Tc  lay  off  Angles  of  60°  and  30°. — Mark  any  number  of 
inches,  say  14,  on  an  indefinite  line.  Place  the  blade 
against  one  extremity  of  this  distance,  and  the  7  inch  mark 
of  the  tongue  at  the  other.  The  tongue  then  forms  an 
angle  of  60°  with  the  indefinite  line,  and  the  blade  an  angle 
of  30°. 

To  Find  the  Bevels  and  Width  of  Sides  and  Ends  of  a 

Square  Hopper. — Fig.  50.  The  large  square  represents  the 
upper  edges  of  the  hopper  and  the  small  one  the  lower 
edges,  or  base.  The  width  of  the  sides  and  ends  is  found 
in  this  way :  Take  the  run  a  b  on  the  tongue,  and  the  per- 
pendicular height  ad  on  the  blade.  It  is  thus  found  in  the 
same  manner  as  the  length  of  a  brace.  To  find  the  cut 
for  a  butt  joint,  take  width  of  side  on  blade  and  half  the 
length  of  the  base  on  tongue ;  the  latter  gives  the  cut.  For 
a  mitre  joint  take  widtli  of  side  on  the  blade  and  perpen- 
dicular height  on  tongue;  the  latter  gives  the  cut. 

For  the  cut  across  the  sides  of  the  boards,  take  the  run 


AND    ITS    USES. 


71 


d  b  on  the  tongue,  and  the  width  of  side  on  blade ;  the 
tongue  gives  the  cut.  The  inside  comers  of  the  sides  and 
ends  are  longer  than  the  outside,  so  if  a  hopper  is  to  be  of 


Fig.  50. 


a  certain  size,  the  lengths  of  ends  and  sides  are  to  be  meas- 
ured on  the  inside  edge  of  each  piece,  and  the  bevels  struck 
across  the  edges  to  these  marks.  This  is  only  in  case  of 
butt  joints.  Of  course  if  the  hopper  is  to  be  square,  the 
thickness  of  the  sides  must  be  taken  from  the  ends. 

Tf  the  top  and  bottom  edges  are  to  be  horizontal,  the 
bevel  is  thus  found :  Take  the  perpendicular  height  of  hop- 
per on  the  blade  and  the  run  on  the  tongue,  the  latter  gives 
both  cuts.  A  hopper  can  be  made  by  the  above  method 
by  getting  the  outside  dimensions  at  top  and  bottom,  and 
the  perpendicular  height. 

Jn  large  hoppers  pieces  are  put  down  along  the  corners 


72  THE    STEEL    SQUARE 

to  Strengthen  them.  The  length,  and  the  bevel  to  lit  the 
corner  are  thus  found :  Suppose  the  top  of  hopper  is  8  feet, 
and  the  bottom  i8  inches  square.  Find  the  diagonals  of 
each,  subtract  the  one  from  the  other,  and  half  the  re- 
mainder is  the  run  for  the  comer  piece.  From  the  length  of 
this  run,  /,  and  the  rise,  a  b,  we  find  the  length  of  the  corner 
piece.  To  find  the  bevel  or  backing,  take  on  the  blade  the 
length  of  the  corner  piece  and  on  the  tongue  the  rise ;  the 
latter  gives  the  bevel.  Another  method  is  to  draw  the  line, 
/,  to  represent  the  seat  of  the  corner  piece,  set  off  square 
with  this  the  line  ;//,  of  the  same  length  as  the  run,  a  b. 
Then  draw  71  o,  which  is  the  length  of  the  corner  piece.  To 
find  the  backing,  draw  a  line,  /,  anywhere  across  /,  at  right 
angles  therewith,  and  at  its  intersection  with  line,  /,  strike 
a  circle  tangent  to  ;/  o.  From  the  point  of  intersection  of 
the  circle  with  /,  draw  lines  to  the  extremities  of  p.  The 
angle  made  by  these  lines  is  the  bevel  or  backing. 

Another  method  generally  employed  for  finding  the 
bevels  of  hoppers  is  to  bevel  the  top  and  bottom  edges  of 
the  sides  and  ends  to  the  angle  they  are  to  stand  at,  then  to 
lay  a  bevel  set  to  a  mitre,  or  angle  of  45°,  on  the  beveled 
edge,  and  that  will  lay  off  a  mitre  joint,  while  a  try-square 
will  lay  oft"  a  butt  joint.  An  angle  of  45°  will  mitre  only 
those  boxes  with  sides  which  are  vertical  and  square  with 
each  other. 

When  the  sides  and  ends  of  a  rectangular  box  or  hopper 
are  of  the  same  width,  that  is,  when  sides  and  ends  slope 
at  equal  angles,  the  bevels,  either  butt  or  mitre,  are  found 
as  for  square  hoppers. 

When  a  hopper  has  the  sides  and  ends  of  different 
widths,  that  is,  when  sides  and  ends  stand  at  different  angles, 


AND     ITS     USES. 


73 


both  having  the  same  rise,  find  the  cuts  for  each  from  its 
respective  rise,  run  and  width. 

Roofing. — Fig.  51.  A  hip-roof  with  two  comers  out  of 
square  is  given  an  example,  the  dimensions  of  which  are : 
width  15  feet,  rise  of  roof  5  feet,  length  30  feet  on  the 


Fig.  51 


shorter  side,  ^;^  feet  on  the  longer.  The  timbers  a  d,  c  d, 
EG,  EG,  are  the  hip  rafters ;  j  j  the  jack  rafters.  The  seats 
of  each  hip  rafter  should  form  a  square,  so  that  each  pair 
of  jack  rafters,  j  j,  for  instance,  may  be  cut  of  equal  length. 


Lengths  and  Bevels  of  Hip-Rafters. — We  will  first  con- 
sider those  on  the  square  end  of  the  roof  In  order  to  find 
their  length,  it  is  first  necessary  to  obtain  their  run,  which 
is  found  as  follows  :  Take  half  the  width  of  building  on  both 
blade  and  tongue,  whence  is  obtained  the  length  of  seat 
from  G  to  E,  at  the  intersection  of  the  dotted  lines.  By  similar 
use  of  the  square,  this  length  with  the  rise  of  roof,  gives 
the  length  of  the  hip-rafter.     The  lengths  of  all  the  rafters 


74  THE    STEEL    SQUARE 

should  be  measured  along  the  middle,  as  the  dotted  lineS 
show.  This  is  the  full  length ;  half  the  thickness  of  the 
ridge-pole  is  to  be  taken  off,  measured  square  back  from 
the  bevel. 

The  bevel  of  the  upper  end  of  a  hip-rafter  is  called  the 
down  bevel.  It  is  always  square  with  the  lower  end  bevel, 
hence  these  bevels  are  found  by  the  parts  taken  on  the 
square  to  find  the  lengths  of  the  hip-rafters.  Another 
method  is  to  take  1 7  inches  on  the  blade  and  the  number 
of  inches  of  rise  to  the  foot,  that  is,  the  rise  in  inches  di- 
vided by  half  the  width  of  roof  in  feet — on  the  tongue.  The 
tongue  gives  the  down  bevel,  the  blade  the  lower  end  bevel. 
The  reason  for  the  foregoing  is  that  when  the  hip-rafters  are 
square  with  each  other,  the  seat  of  the  hip  is  the  diagonal 
of  a  square  whose  side  is  half  the  width  of  building.  The 
diagonal  of  a  square  with  a  i  2  inch  side  is  1 7  inches  nearly. 
So  if  the  rise  of  roof  in  i  foot  is  6  inches,  the  rise  of  hip- 
rafter  will  be  that  only  in  17  inches.  The  directions  here 
given  assume  that  the  hip-rafter  abuts  the  ridge-pole  at  right 
angles,  but  as  the  ground  plan  of  the  roof  shows  that  they 
meet  at  an  acute  angle,  another  bevel  must  be  considered, 
called  the  side  bevel  of  the  hip-rafters.  Were  there  no  slope 
to  the  roof,  the  bevel  where  they  meet  the  ridge  pole  would 
bean  angle  of  45°,  as  the  hips  would  be  square  with  each 
other.  When  a  pitch  or  slope  is  given,  the  hips  depart  from 
the  right  angle,  and  therefore  the  side  bevels  are  always 
less  than  45°.  Take  the  length  of  hip  on  the  blade,  and 
its  run  on  the  tongue ;  the  blade  gives  the  cut. 

Backing  of  the  hip-rafters.  The  backs  of  the  hip-rafters 
must  be  beveled  to  lie  even  with  the  planes  of  the  roof 
This  bevel  must  slope  from  the  middle  toward  either  side. 


AND    ITS    USES.  75 

It  IS  found  by  taking  the  length  of  hip  on  blade,  and  the 
rise  of  the  roof  on  tongue.     The  latter  gives  the  bevel. 

To  find  the  lengths  of  the  jack-rafters  :  Suppose  there 
are  to  be  four  between  the  corner  and  the  first  common 
rafter;  then  there  are  five  spaces,  which,  by  dividing  7  foot 
6  inches  by  5,  are  i  foot  2  inches  from  centre  to  centre  of 
jacks.  The  rise  of  roof,  also  divided  by  5,  gives  i  foot  rise 
for  the  shortest  rafter.  The  run  is  i  foot  6  inches ;  as  both 
rise  and  run  are  given,  the  length  down  and  lower  bevels 
are  found  therefrom.  The  next  jack  has  double  the 
rise,  run  and  length  of  the  first ;  the  following  one  three 
times,  and  the  fourth  four  times.  All  the  measurements 
are  to  proceed  on  or  from  the  middle  lines  of  the  jacks. 

The  side  bevel  of  all  the  jack-rafters  is  obtained  by  taking 
the  length  of  a  common  rafter  on  the  blade  and  its  run  on 
the  tongue ;  the  bevel  on  the  blade  gives  the  result. 


Fig.    52. 

Let  us  now  consider  the  end  of  the  building  out  of  square. 
Fig.  52  illustrates  the  method  of  laying  down  the  seats  of 
the  hips.  To  find  the  lengths  of  these  hips,  the  lengths  of 
the  seats  must  be  got  by  taking  half  the  width  of  building 
on  blade,  and  the  distance  from  the  end  of  the  dotted  line 
crossing  the  roof,  to  the  corner  on  the  tongue.    The  length 


•j6  THE    STEEL    SQUARE 

of  the  seat  so  obtained  taken  on  the  square,  with  the  rise  of 
the  roof,  gives  the  length  of  the  respective  hip-rafter. 

The  down  and  lower  end  bevels  are  found  as  in  the  pre- 
vious hip-rafters.  To  obtain  each  side  bevel,  add  the  dis- 
tance from  the  dotted  line  to  the  corner  and  the  gain  of 
the  hip-rafter ;  take  the  sum  on  the  blade,  and  half  the  width 
of  building  on  the  tongue ;  the  latter  gives  the  cut. 

The  lengths,  etc.,  of  the  jack-rafters  on  the  side,  are  de- 
termined as  at  the  square  end  of  the  roof;  the  side  bevel 
being  found  by  taking  the  length  of  a  common  rafter  on 
the  blade,  and  the  distance  from  the  dotted  line  to  corner 
on  the  tongue.     The  latter  showing  the  bevel. 

The  lengths  of  jack-rafters  on  the  end.  Assuming  there 
are  to  be  four  jacks  between  the  corner  and  the  centre  in- 
cluded, half  the  length  of  the  end  of  the  roof  must  be  di- 
vided by  5.  One  side  of  the  roof  being  3  feet  longer  than 
the  other,  we  place  3  feet,  on  tongue,  and  1 5  feet,  the  width 
of  building,  on  the  blade,  and  thus  obtain  the  distance  from 
corner  to  corner  on  the  end  of  the  roof.  Half  this  divided 
by  5  gives  the  distance  of  the  jacks  apart.  The  distance 
from  where  the  middle  lines  of  the  hips  meet  to  the  middle 
point  of  the  end  of  the  roof  is  also  to  be  divided  by  5,  the 
quotient  giving  the  run  of  the  shortest  rafter.  The  rise  is 
the  same  as  for  the  jacks  on  the  square  end. 

These  rules  give  the  full  length  of  rafter,  so  that  when 
hips  come  against  a  ridge-pole  or  jacks  against  a  hip,  half 
the  thickness  of  pole  or  hip,  squared  back  from  their  down 
bevels,  must  be  taken  off 

Side  bevels  of  these  jacks  are  obtained  by  adding  the 
distance  from  the  dotted  line  to  the  corner  to  the  gain  of 
a  common  rafter  in  running  that  distance ;  take  this  on  the 


AND     ITS     USES. 


77 


blade,  and  half  the  width  of  building  on  the  tongue.     The 
blade  gives  the  bevel. 

Trusses. — Fig.  53.  a  is  the  straining  beam,  v.  the  brace, 
T  the  tie  beam.  Generally  the  brace  has  about  one-third 
the  length  of  tie  beam  for  a  run.  From  the  rise  and  run 
find  the  length  and  lower  end  bevel  of  the  brace.  After 
marking  the  lower  end  bevel  on  the  stick,  add  to  it  just 
what  is  cut  out  of  the  tie  beam.  The  bevel  of  the  upper 
end  of  the  brace  where  it  butts  against  the  straining  beam 
is  found  in  the  following  manner.     Take  the  length  of  the 


Fig.  53. 

brace,  or  a  proportional  part,  and  mark  it  on  the  edge  of  a 
board ;  take  half  the  rise  of  the  brace  on  the  tongue,  lay  it 
to  one  of  these  marks  on  the  board,  and  move  the  blade 
till  it  touches  the  other  mark  on  board.  A  line  drawn 
along  the  tongue  gives  the  bevel  for  both  brace  and  strain- 
ing beam.  The  angle  made  between  brace  and  strain- 
ing beam  is  thus  bisected.  Lay  off  the  measurements  from 
the  outside  of  the  timbers.  Put  a  bolt  where  shown,  with 
a  washer  under  the  head  to  fit  the  angle  of  straining 
t)eam  and  brace, 


78 


THE    STEEL    SQUARE 


'lliere  are  quite  a  number  of  methods  of  obtaining  ap- 
proximate proportions  of  the  diameter  of  circles  to  their 
circumferences.  The  true  proportion,  or,  as  it  is  some- 
times expressed,  "  the  squaring  of  the  circle,"  is  one  of 
those  feats,  like  the  discovery  of  "  perpetual  motion,"  and  is 
as  far  from  being  accomplished  now  as  ever.  At  any  rate, 
it  makes  but  little  difference  at  this  time,  to  the  operative 
mechanic,  whether  the  circle  can  be  squared  or  not,  so 
long  as  he  can  get  near  enough  to  the  truth  to  satisfy  the 
requirements  at  hand  satisfoctorily ;  and  to  aid  him  in  this, 
the  following  method  is  shown  of  obtaining  the  circum- 
ferences of  circles  when  the  diameter  is  given,  by  use  of 
the  .square.  Of  course,  as  shown  in  the  cut,  the  rule  will 
apply  to  circles  of  any  reasonable  dimensions. 


Fig.  54. 

Let  A  B,  Fig.  54,  be  a  straight  line,  or  the  straight  edge 
of  a  board ;  then  apply  the  square  as  shown,  placing  the 
16-inch  mark  on  the  blade  at  c,  and  the  5-inch  mark  on 
the  tongue  at  u.  See  that  the  junctions  of  the  blade  and 
tongue  of  the  square  with  the  line  a  b,  are  accurately 
placed,  for  on  this  depends  the  truth  of  the  results.  Now, 
suppose  we  wish  to  ascertain  the  circumference  of  a  circle 


AND    ITS    USES.  79 

whose  diameter  is  8  inches ;  commencing  at  the  point,  c, 
we  space  off  the  diameter,  8  inches,  three  times,  on  the  hne 
c  o,  as  shown  at  8"  8"  8" ;  then  square  down  the  hne  8"  f, 
then  c  F  will  be  the  circumference  of  a  circle  whose  diam- 
eter is  8.  It  will  be  seen,  by  dotted  lines  in  the  cut,  that 
tiie  circumference  equals  the  diagonal  of  a  rectangle  whose 
sides  are  respectively  24  and  7H  inches;  so  that  by  adopt- 
ing these  figures  (24  and  7;)?)  it  enables  the  operative  to 
use  the  full  length  and  capacity  of  the  square.  The 
better  way,  however,  is  to  work  from  a  basis  of  16  and  5, 
anil  draw  the  lines,  c  o  and  A  b,  to  considerable  length,  so 
that  tliey  may  be  made  available  fjr  dimensions  beyond 
the  range  of  the  square.  Now,  let  us  suppose  an  instance 
where  the  circumference  of  a  circle  is  wanted,  whose  diam- 
eter is  10;  we  simply  space  off  three  tens,  or  thirty  inches, 
on  the  line  c  O;  which,  in  this  case,  is  at  k.  Square  down 
from  K  to  R,  and  c  R  is  the  length  sought. 

Now,  to  prove  this,  let  us  proceed  as 'follows:  Diam.  = 
10  X  3'i4i6  =  31-4160,  or  nearly  thirty-one  inches  and 
fifteen  thirty-seconds  of  an  inch.  Now,  if  we  measure  c  R, 
we  will  find  that  the  distance  is  exactly  3 1  -4 :  60  inches, 
and  is,  therefore,  the  answer  sought.  It  will  be  seen  by 
these  examples  that  the  circumferences  of  circles  may  be 
easily  obtained  when  the  diameters  are  known.  So,  also, 
may  the  diameters  be  found  when  the  circumferences  are 
known,  for  by  laying  off  the  circumference  on  the  line  A  B, 
as  c  D  in  Fig.  54,  •  for  instance,  and  then  applying  the 
square  as  there  exhibited,  and  dividing  the  distance  from 
the  heel  of  the  square  to  the  point  c  into  three  equal  parts. 
One  of  these  parts  is  the  diameter  of  the  circle  whose  cir- 
cumference equals  the  distance  from  c  to  d. 


8o 


THE    STEEL    SQUARE 


In  my  experience,  I  have  frequently  been  asked  how  a 
mitre,  or  equal  joint,  could  be  laid  off  by  using  the 
square. 

'I'he  matter  is  so  simple,  that  it  was  thought  unnecessary 
to  insert  it  in  the  first  edition,  but  the  many  inquiries  on 
the  subject  that  have  been  received  since  the  work  was 
published,  induces  me  to  give  a  few  examples  of  the  man- 
ner in  which  advanced  workmen  generally  accomplish 
this  end.     Let  Fig.  55  represent  an  oblique  angle  formed 


Fig.  ss. 

by  two  parallel  boards.  To  obtain  the  joint,  a,  space  off 
equal  distances  from  the  point  i  to  3,  3,  then  square  over 
from  the  lines,  r,  r,  keeping  the  heel  of  the  square  at  the 
points,  3,  3.  At  the  junction  of  the  lines  formed  by  the 
tongue  of  the  square  at  o  will  be  one  point,  and  i  will  be 
the  other  by  which  the  joint  line.  A,  is  defined. 

To  find  the  line^of  juncture  for  an  acute  angle,  we  pro- 
ceed as  follows :  Fig.  56  represents  two  parallel  boards; 
I  the  extreme  angle,  3,  3  equal  distances  from  the  angle  i 
and  are  the  points  where  the  heel  of  the  square  must  rest 
to  form  the  lines  o,  3  ;  o  shows  the  junction  of  the  lines 
formed  by  the  blade  of  the  square.  Draw  a  line  from  p  to 
I,  and  the  line,  a,  formed,  is  the  bevel  require^' 


AND    ITS    USES. 


Si 


Fig.  s6. 

It  will  be  seen,  by  these  two  examples,  that  the  bevel  of 
a  junction  at  any  angle  may  be  obtained  by  this   method. 

Sometimes,  when  estimating  on  work,  it  becomes  neces- 
sary to  get  the  length  of  braces  and  other  timbers,  that 
would  reauire  considerable  figuring  to  obtain  if   the  usual 


Fig.  57. 

method  of  finding  the  length  of  the  third  side  of  a  right- 
angled  triangle  was  adopted.  The  square,  at  this  juncture, 
may  be  made  use  of  with  advantage,  where  the  length  of 
the  lines  wanted  is  within  the  range  of  the  instrument,  and 
almost  any  dimensions  may  be  manipulated,  by  making  the 
subdivisions  of  the  inch  represent  inches,  feet,  or  yards. 
Suppose  we  want  to  get  the  length  of  a  brace  with  unequal 
run  of  7  and  12  feet  respectively.     Lay  the  two-foot  rule 


$2  THE    STEEL    SQUARE 

across  the  square,  putting  the  end  on  7  on  the  tongue,  and 
cutting  the  12-inch  hne  on  the  blade;  then,  as  shown  in 
Fig.  57,  we  will  have  on  the  side  of  the  rule  a  b,  13  feet 
II  inches,  or  say  14  feet,  \vhich  is  near  enough  for  the 
estimator's  purpose,  and  if  required  for  working  purposes, 
the  exact  length  and  bevels  may  be  obtained  by  careful 
measurement. 

Conclusion. — The  ingenious  and  intelligent  workman, 
after  thoroughly  mastering  the  foregoing  applications  of  the 
"  Steel  Square,"  will  awaken  to  the  fact  that  the  tool  may 
be  used  for  the  solution  of  a  thousand  and  one  little 
matters  that  will  crop  up  in  his  every-day  calling,  and  by 
a  combination  or  adaptation  of  the  rules  presented,  he  will 
be  able  to  overcome  all  ordinary  difficulties  in  obtaining 
cuts,  bevels,  and  Imes  for  roofs,  hoppers,  mouldings,  etc. 


AND    ITS    USES.  83 


PART  IV. 
Miscellaneous  Rules  and  Memoranda. — The   practical 

car|)cnter  and  joiner  will  frequently  want  to  use  the  more 
elaborate  methods  of  obtaining  solutions  where  the  prob- 
lems are  complicated  and  various ;  and  the  following  rules 
are  inserted  in  this  work  with  a  view  of  reaching  some  of 
the  problems  that  appear  to  be  beyond  the  range  of  the 
Sceel  Square  without  making  such  intricate  combinations 
as  would  be  sure  to  lead  to  confusion  in  ordinary  hands. 

Hip-Roofs. — The  principles  to  be  determined  in  a  hip- 
roof are  seven  ;    namely  : 

ist.  The  angle  which  a  common  rafter  makes  with  the 
level  of  the  \.o\)  of  the  building ;  that  is,  the  pitch  of  the  roof. 

2nd,  The  angle  wliich  the  hip-rafter  makes  with  the  level 
of  the  building. 

3d.  The  angles  which  the  hip-rafter  makes  with  the  ad- 
joining sides  of  the  roof  This  is  called  the  backing  of 
the  hip. 

4tli.  The  height  of  the  roof,  or  the  "  rise,"  as  it  is  called. 

5lh.  The  lengths  of  the  common  rafters. 

6th.  The  lengths  of  the  hip-rafters. 

7th.  The  distance  between  the  centre  line  of  the  hip- 
rafter  and  the  centre  line  of  the  first  entire  common  rafter. 

The  first,  fourdi,  fifth  and  seventh  are  generally  given, 
and  from  these  the  others  may  be  found,  as  will  be  shown 
by  the  following  illustrations :      Let  a  B  c  D  Fig.  58,  be 


84 


THE    STEEL   SQUARE 


the  plan  of  a  roof.  Draw  g  h  parallel  to  the  sides,  A  d, 
B  c,  and  in  the  middle  of  the  distance  between  them. 
From  the  points  A,  B,  c,  d,  with  any  radius,  describe  the 
curves  ab,  a  b,  cutting  the  sides  of  the  plan  at  a,  b.  From 
these  points,  with  any  radius,  bisect  the  fot  angles  of  the 
plan    at    r,  r,  r,  t,  and  from  A,  B,  c,  D,  through  the  points, 


D 

e                  ■% 

io, 

1 

. 

\ 

^,>;^ 

\ 

\, 

\ 

\ 

/" 

^< 

'■Z 

^ — :A^ 

X- 

/ 

-y 

\^     I 

7 

\ 

I 

/ 

- 

/,i 

■f- 

\ 

\ 

i 

/> 

»       f 

r 

i 

0/ 

U 

Fig.  58. 

r,  r,  r,  r,  draw  the  lines  of  the  hip-rafters,  a  G,  b  G,  c  H,  D  H, 
cutting  the  ridge-line,  g  h,  in  g  and  H,  and  produce  them 
indefinitely.  The  dotted  lines,  c  e,  df,  are  the  seats  of  the 
last  entire  common  rafters.  Through  any  point  in  the 
ridge-line,  i,  draw  e  i  f  at  right  angles  to  g  h.  Make  i  k 
equal  to  the  height  or  rise  of  roof,  and  join  e  k,  f  k;  then 
E  K  is  the  length  of  a  common  rafter.  Make  go,  ho, 
equal  to  i  k,  the  rise  of  the  roof,  and  join  a  <?,  b  ^,  c  ^,  D  ^, 
for  the  length  of  the  hip-rafters.  If  the  triangles,  a  <?  G,  b  ^  g, 
be  turned  round  their  seats,  a  G,  B  G,  until  their  perpen- 
diculars are  perpendicular  to  the  plane  of  the  plan,  the 
points,  o  o,  and  the  lines,  g  0,  G  0,  will  coincide,  and  the 
rafters,  a  ^,  b  ^,  be  in  their  true  positions. 


AND    ITS    USES. 


85 


If  the  roof  is  irregular,  and  it  is  required  to  keep  tlie 
ridge  level,  we  proceed  as  shown  in  Fig.  59. 

Bisect  the  angles  of  two  ends  by  the  lines  k  b,  n  b,  c  G, 
D  G,  in  the  same  manner  as  in  Fig.  58;  and  through  g 
draw  the  lines   g  E,  G  F,  parallel  to  the  sides,  c  B,  d  a,  re- 


FlG.    59. 

spectively  cutting  a  b,  b  b,  in  e  and  f  ;  join  e  f  ;  then  the 
triangle,  E  G  F,  is  a  flat,  and  the  remaining  triangle  and 
trapeziums  are  the  inclined  sides.  Join  g  b,  and  draw  h  i 
perpendicular  to  it ;  at  the  points  M  and  N,  where  H  i  cuts 
the  lines  g  e,  g  f,  draw  m  k,  N  l  perpendicular  to  h  i,  and 
make  them  equal  to  the  rise ;  then  draw  H  K,  i  l  for  the 
lengths  of  the  common  rafters.  At  E,  set  up  E  m  perpen- 
dicular to  B  E ;  make  it  equal  to  u  k  or  N  L,  and  join  b  ;;/ 
for  the  length  of  the  hip-rafter,  and  proceed  in  the  same 
manner  to  obtain  a  ;;/.  c  w.  d  ;;/. 

To  find  the  backing  of  a  hip-rafter,  when  the  plan  is 


86 


THE    STEEI-    SQUARE 


right-angled,  we  proceed  as  shown  in  Fig.  60.  Let  bI>,  l>c 
be  the  common  rafters,  A  D  the  width  of  the  roof,  and  a  b 
equal  to  one-half  the  width.  Bisect  b  c  in  a,  and  join  a  a, 
D  a.     From  a  set  off  a  c,  a  d  equal  to  the  height  of  the 


Fig.  60. 


rooT  a  l>,  and  join  a  tf,  T)c;  then  Ad,  Dr  are  the  hip- 
rafters.  To  find  the  backing :  from  any  point  //  in  a  d, 
draw  the  perpendicular  /i  g,  cutting  a  a  in  g;  and  through 
,i^  draw  perpendicular  to  a  a  the  line  e/,  cutting  A  B,  a  D 
in  e  and/  Make  g  k  equal  to  g  h,  and  join  k  c,  kf;  the 
angle  e  Z'/is  the  angle  of  the  backing  of  the  hip-rafter  c. 

Fig.  61  shows  the  method  of  obtaining  the  backing  of 
the  hip  where  the  plan  is  not  right  angled. 

Bisect  A  D  in  a,  and  from  a  describe  the  semicircle 
A  b  T>;  draw  a  h  parallel  to  the  .sides  A  b,  d  c,  and  join 
\  byj)  b,  for  the  seat  of  the  hip-rafters.     From  b  set  ofif  on 


AND    ITS    USES. 


87 


b  x^  b  B  the  lengths  b  d,  b  e,  equal  to  the  height  of  the  roof 
b  c,  and  join  a  ^,  d  d,  for  the  lengths  of  the  hip-rafters.  To 
find  the  backing  of  the  rafter: — In  a  e,  take  any  point  k, 
and  draw  k  h  perpendicular  to  a  e.  Through  //  draw//^  g 
perpendicular  to  a  b^  meeting  a  b,  a  d  in/and^.  Make 
//  /  equal  to  h  k,  and  join  //,  g  /;  t\\Q  fig  is  the  backing 
of  the  hip. 


Fig.  61. 

Fig.  62  shows  how  to  find  the  shoulder  of  purlins: 
First,  where  the  purlin  has  one  of  its  faces  in  the  plane 
o:  the  roof,  as  at  e.  From  c  as  a  centre,  with  any  radius, 
describe  the  arc  d g;  and  from  the  opposite  extremities  of 
the  diameter,  draw  d  //,  g  m  perpendicular  to  r.  c.  From 
e  and/,  where  the  upper  adjacent  sides  of  the  purlin  pro- 
duced cut  the  curve,  draw  ei,f  I  parallel  to  d  //,  g  m  ;  also 
draw  c  k  parallel  to   d  h.     From  /  and  /  draw  /  ///  and  i  h 


88 


THE    STEEL    SQUARE 


Fig.  62. 


EiG.  63. 


AND    ITS    USES. 


89 


parallel  to  b  c,  and  join  k  //,  k  m.  Then  c km  is  the  down 
bevel  of  the  purlin,  and  c  k  h  is  its  side  bevel. 

When  the  purlin  has  two  of  its  sides  parallel  to  the 
horizon.  This  simple  case  is  shown  worked  out  at  f.  It 
requires  iio  explanation. 

When  the  sides  of  the  purlin  make  various  angles  with 
the  horizon.  Fig.  6^^  shows  the  application  of  the  method 
described  in  Fig.  62  to  these  cases. 

It  sometimes  happens,  particularly  in  railroad  buildings, 
that  the  carpenter  is  called  upon  to  pierce  a  circular  or 
conical    roof  with  a  saddle  roof,  and  to  accomplish  this 


Fig.  64. 


economically  is  often  tlie  result  of  much    labor    and  per- 
plexity if  a  correct  method  is  not  at  hand. 

The  following  method,  shown  in  Fig.  64,  is  an  excellent 


go  THE    STEEL   SQUARE 

one,  and  will  no  doubt  l)e  found  useful  in  cases  such  as 
mentioned. 

Let  I)  H,  F  H  be  the  common  rafters  of  the  conical  roof, 
and  K  L,  I  L  the  common  rafters  of  the  smaller  roof,  both 
of  the  same  pitch.  On  g  h  set  up  g  e  equal  to  m  l.  the 
height  of  the  lesser  roof,  and  draw  e  d  parallel  to  d  f, 
and  from  d  draw  c  d  perpendicular  to  d  f.  The  triangle 
D  d  c,  will  then  by  construction  be  equal  to  the  triangle 
K  L  M,  and  will  give  the  seat  and  the  length  and  pitch  of 
the  common  rafter  of  the  smaller  roof  B.  Divide  the  lines 
of  the  seats  in  both  figures,  d  r,  k  m,  into  the  same  number 
of  equal  parts;  and  through  the  points  of  division  in  e, 
from  G  as  a  centre,  describe  the  curves  c  a,  2  g,  if,  and 
through  those  in  b,  draw  the  lines  3/4  g,  m  a,  parallel  to 
the  sides  of  the  roof,  and  intersecting  the  curves  in /^«. 
Through  these  points  trace  the  curves  cfga,Afga, 
which  give  the  lines  of  intersection  of  the  two  roofs.  Then 
to  find  the  valley  rafters,  join  c  a,  a  a;  and  on  a  erect  the 
lines  a  b,  a  b  perpendicular  X.o  Q.  a  and  a  a,  and  make  them 
respectively  equal  to  M  L ;  then  cb,  hbi's.  the  length  of  the 
valley  rafter,  very  nearly. 

Fig.  65  shows  how  a  curved  hip-rafter  may  be  obtained- 
The  rafter  shown  in  this  instance  is  ogee  in  shape,  but  it 
makes  no  difference  what  shape  the  common  rafter  may 
1)6,  the  proper  shape  and  length  of  hip  may  be  obtained  by 
tliis  method.  It  will  be  noticed  that  one  side  of  the  example 
shown  is  wider  than  the  other;  this  is  to  show  diat  the  rule 
will  work  correctly  where  the  sides  are  unequal  in  width, 
as  well  as  where  they  are  equal.  Let  a  b  c,  f  e  c  repre- 
sent the  plan  of  the  roof,  f  c  g  the  profile  of  the  wide 
side  of  the  rafter.     First,  divide  this  rafter  g  c   into  any 


AND    ITS    USES. 


9« 


number  of  parts — in  tliis  case  six.  Transfer  these  points  to 
the  mitre  line  e  b,  or,  what  is  the  same,  the  hne  in  the  plan 
representing  the  hip  rafter.  From  the  points  thus  estab- 
Hshed  in  e  b,  erect  perpendiculars  indefinitely.  With  the 
dividers  take  the  distance  from  the  points  in  the  line  F  c, 


measuring  to  the  points  in  the  profile  G  c,  and  set  the  same 
off  on  corresponding  lines,  measuring  from  e  b,  thus  estab- 
lishing the  points  i,  2,  3,  etc.;  then  a  line  traced  through 
these  points  will  be  the  required  hip  rafter. 

For  the  common  rafter  on  the  narrow  side,  continue  the 
lines  from  e  b  parallel  with  the  lines  of  the  plan  d  e  and 
A  B.  Draw  A  D  at  right  angles  to  these  lines.  With  the 
dividers  as  before,  measuring  from  f  c  to  the  points  in 
G  c,  set  off  corresponding  distances  from  a  d,  thus  estab- 


92 


THE    STEEL    SQUARE 


lishing  the  points  shown  between  a  and  H.  A  Hne  traced 
through  the  points  thus  obtained  will  be  the  line  of  the 
rafter  on  the  narrow  side.  This  is  supposed  to  be  the 
return  roof  of  a  veranda,  but  is  only  shown  as  an  example, 
for  it  is  not  customary  to  build  verandas  nowadays  with  an 
ogee  roof,  but  with  a  rafter  having  a  depression  or  cove  in 
it.     For  accuracy  it  would  be  as  well  to  make  nearly  twice 


Fig.  66. 


the  number  of  divisions    shown  from  i  to  6,  as  are  there 
represented. 

It  has  been  shown,  in  the  forepart  of  this  work,  how  the 
bevels  and  lines  for  hoppers  may  be  obtained  by  the  aid  of 


AND    ITS    USES. 


93 


the  square,  and  it  is  now  proposed  to  show  how  the  same 
results  may  be  obtained  by  a  system  of  Unes.  This 
method,  in  many  shapes  and  forms,  has  been  used  from 
time  immemorial  by  workmen,  more  particularly  by  car- 
riage makers  to  obtain  the  bevels  of  splayed  seats;  the 
present  way  of  expressing  it,  however,  is  comparatively 
recent. 

If  we  make  a  i.  Fig.  66,  represent  the  elevation  of  our 
hopper,  and  B  i  a  portion  of  the  plan,  we  proceed  as 
follows :  Lay  off  n  s,  which  is  the  bevel  of  one  side,  and 
N  s  p  o  the  section  of  one  end. 

Place  one  foot  of  the  dividers  at  n,  and  with  N  s  as 
radius  describe  the  arc  s  u,  intersecting  the  right  line  n  u 
in  the  point  u.  At  s  erect  the  perpendicular  s  t,  and  draw 
the  line  u  x  at  right  angles  to  N  u.  Connect  n  and  x ; 
then  the  triangle  m  n  t  is  the  end  bevel  required.  The 
line  N  X  is  the  hypothenuse  of  a  right-angled  triangle,  of 
which  N  u  may  may  be  taken  for  the  perpendicular  and 
u  X  for  the  base.  To  find  the  mitre  of  which  d  e  is  the 
plan,  project  s  and  p,  as  indicated  in  the  plan  by  the  full 
lines.  With  s  p  as  radius  and  s  as  centre,  describe  the  arc 
p  R.  In  the  plan  draw  D  G,  on  which  lay  off  the  distance 
s  R,  measuring  from  f,  as  shown  by  F  G.  Then  j  h  f  is 
the  mitre  sought. 

Fig.  67  shows  the  rule  for  finding  the  bevels  for  the 
sides  of  the  hopper.  From  m,  the  point  at  which  e  m  in- 
tersects B  c,  or  the  inner  face  of  the  hopper,  erect  the  per- 
pendicular M  L,  intersecting  r  f,  or  the  upper  edge  of  the 
hopper,  in  the  point  l.  Then  l  c  shows  how  much  longer 
the  inside  edge  is  required  to  be  than  the  outside.  In  the 
plan  draw  x  v  parallel  to  s  x,  making  the  distance  between 


94 


THE    STEEL    SQUARE 


the  two  lines  equal  to  c  F  of  the  elevation,  or,  equal  to  the 
thickness  of  one  side.     From  the  point  l  in  the  elevation 


drop  the  line  l  w,  producing  it  until  it  cuts  the  mitre  line 
N  o,  as  shown  at  w.  From  w,  at  riglit  angles  to  l  w, 
erect  the  perpendicular  w  v,  meeting  the  line  T  v  in  the 
point  V.  Connect  v  and  u;  then  t  v  u  will  be  the  angle 
sought.  This  Ijevel  may  be  found  at  once  by  laying  off 
the  thickness  of  the  side  from  the  line  e  m,  as  shown  by 
N  p  in  the  elevation,  and  ap[)lying  the  bevel  as  shown. 
This  course  does  away  with  the  plan  entirely,  provided 
both  sides  have  the  same  inclination. 


AND    ITS    USES. 


95 


There  are  several  other  \va\'s  by  w  hicli  the  same  results 
may  be  obtained;  some  of  these  will  no  doubt  occur  to 
the  reader  when  laying  out  the  lines  as  shown  here. 

Fig.  68  exhibits  a  method  of  obtaining  the  correct  shape 
of  a  veneer  for  covering  the  splayed  head  of  a  gothic  jamb. 


E  shows  the  horizontal  sill,  ^/the  S[)lay,/A  the  line  of  the 
inside  of  jamb,  o  the  difference  between  front  and  back 
edges  of  jamb,  B  a  the  line  of  splay.  At  the  point  of  junc- 
tion of  the  lines  b  a, /a,  set  one  point  of  the  compasses, 
and  with  the  radius  a  b  draw  the  outside  curve  of ;/ ;  then 
with  the  radius  a  s  draw  the  inside  curve,  and  //  will  be  the 
veneer  required.  This  will  give  the  required  shape  for 
either  side  of  the  head. 


PRACTICAL  BOOKS  FOR  PRACTICAL  MEN. 

The  Steel  Square  and  Its  Uses.    By  Hodgson. 

Second  and  Enlarged   Edition. $1.00 

This  is  the  only  complete  work  on  The  Steel  Square  and  Its  Uses  ever  published. 
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ordinary  intelligence,  can  understand  it  from  "end  to  end. 

The  new  edition  is  illustrated  with  over  seventy-live  wood  cuts,  sliowing  how 
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Carpentry. 

Stair-Building  Made  Easy. 

Being  a  Full  and  Clear  Description  of  the  Art  of  Building  the  Bodies,  Car- 
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is  added  an  Illustrated  Glossary  of  Terms  used  in  Stair-Building,  and  Designs 
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This  work  takes  hold  at  the  very  beginning  of  the  subject,  and  carries  the 
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A  New  System  of  Hand-Railing. 

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An  Old  Stair-Builder.  Edited  and  Corrected  by  Fred.  T.  Hodgson. 
Cloth,  Gilt, $1.00 

The  Workshop  Companion. 

A  Collection  of  Useful  and  Reliable  Recipes,  Rules,  Processes,  Methods, 
Wrinkles  and  Practical  Hints  for  the  Household  and  the  Shop.    Neatly 

Bound, 35c. 

This  is  a  book  of  164  closely  printed  pages,  forming  a  Dictionary  of  Practical 
Information,  for  Mechanics,  Amateurs,  Hotisekeepers,  Farmers,  Everybody.  It 
is  not  a  mere  collection  of  newspaper  clii^pings.  but  a  series  of  original  treatises 
on  various  subjects,  such  as  Alloys,  Cements,  Inks,  Steel,  Signal  Lights,  Polish- 
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Iron,  Steel,  Glass,  etc. 


Drawing  Instruments. 

Being  a  Treatise  on  Draughting  Instruments,  with  Rules  for  their  Use  and 
Care,  Explanations  of  Scale,  Sectors  and  Protractors.  Together  with  Memo- 
oranda  for  Draughtsmen,  Hints  on  Purchasing  Paper,  Ink,  Instruments, 
Pencils,  etc.  Also  a  Price  List  of  all  materials  required  bv  Draughtsmen. 
Illustrated  with  Twenty-four  Explanatorv  IllustiiUions.  *  By  Fred.  T. 
Hodgson.    Paper, --...■.        250. 


Practical  Carpentry. 

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and  Laying-  Out  of  all  kinds  of  Carpenters'  and  Joiners'  Work.  With  the 
solutions  of  the  various  problems  in  Hip-Roofs,  Gothic  Work,  Cenleriu":, 
Splayed  Work,  Joints  and  Jointin<r,  Hinging,  Dovetailing,  Mitering,  Timber 
Splicing,  Hopper  Work,  Skylights,  Raking  Mouldings,  Circular  Work,  etc.. 
etc.,  to  which  is  pretixed  a  thorough  treatise  on  '"Carpenter's  Geometry." 
By  Fred.  T.  Hodgson,  author  of  "  The  Steel  Square  and  Its  Uses,"  "  The 
Builder's  Guide  and  Estimator's  Price  Book,"  ''  The  Slide  Rule  and  How  to 

Use  It,"  etc.,  etc.    Cloth,  Gilt, $1.00 

This  is  the  most  complete  book  of  the  kind  ever  published.    It  is  thorough, 

practical  and  reliable,  and  at  the  same  time  is  written  in  a  style  so  plain  that 

any  workman  or  apprentice  can  easily  understand  it. 

Hand  Saws. 

Their  Use,  Care  and  Abuse.  How  to  Select  and  How  to  File  Them.  By 
Fred.  T.  Hodgson,  author  of  "The  Steel  Square  and  Its  Uses,"  "The 
Builder's  Guide  and  Estimator's  Price  Book,"  "  Practical  Carpentry,"  etc., 
etc.  Illustrated  by  Over  75  Engravings.  Being  a  Complete  Guide  for 
Selecting,  Using  and  Filing  all  kinds  of  Hand  Saws,  Back  Saws,  Compass 
and  Key-hole  Saws,  Web,  Hack  and  Butcher's  Saws  ;  showing  the  Shapes, 
Forms,  Angles,  Pitches  and  Sizes  of  Saw  Teeth  suitable  for  all  kinds  of 
Saws,  and  for  all  kinds  of  Wood,  Bone,  Ivory  and  Metal ;  together  with  Hints 
and  Suggestions  on  the  clioice  of  Files,  Saw  Sets,  FiBng  Clamps,  and  other 
matters  pertaining  to  the  care  and  management  of  all  classes  of  hand  and 

other  small  saws.    Cloth,  Gilt, $1.00 

The  work  is  intended  more  particularly  for  operative  Carpenters,  Joiners, 

Cabinet  Makers,  Carriage  Builders  and  Wood  Workers  generally,  amateurs  or 

professionals. 

Plaster :    How  to  Make,  and  How  to  Use. 

Illustrated  with  numerous  engravings  in  the  text,  and  Three  Plates,  giving 
some  Forty  Figiu'es  of  Ceilings,  Centrepieces,  Cornices,  Panels,  and  Soffits. 
Being  a  complete  guide  for  the  plasterer,  in  the  preparation  and  application 
of  all  kinds  of  Plaster,  Stucco,  Portland  Cements,  Hydraulic  Cements,  Lime 
of  Tiel,  Rosendale  and  other  Cements.  To  which  is  added  an  Illustrated 
Glossary  of  Technical  Terms  used  by  plasterers,  with  hints  and  suggestions 
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The  Builder's  Guide  and  Estimator's  Price  Book. 

Being  a  Compilation  of  Current  Prices  of  Lumber,  Hardware,  Glass, 
Plumbers'  Supplies,  Paints,  Slates,  Stones,  Limes,  Cements,  Bricks,  Tin, 
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ing the  Several  Kinds  of  Work  Required  in  Building.  Together  with  Prices  of 
Doors,  Frames,  Sashes,  Stairs,  Mouldings,  Newels,  and  other  Machine  Work. 
To  which  is  appended  a  large  luimber  of  Building  Rules,  Data,  Tables,  and 
Useful  Memoranda,  with  a  (Glossary  of  Architectural  and  Building  Terms. 
By  Fred.  T.  Hodgson,  Editor  of  "The  Builder  and  Wood-Worker,"  Author 
of  "  The  Steel  Square  and  Its  Uses,"  etc.,  etc.    I'irao.,  Cloth,       -       $2.00 


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Mechanical  Draughting. 

The  Student's  Illustrated  Guide  to  Practical  Draughting.  A  .series  of  Prac- 
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This  is  a  simple  but  thorough  book,  by  a  draughtsman  of  twenty-five  years" 
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those  who  pursue  the  study  under  the  direction  of  a  teacher. 

Lectures  in  a  Workshop. 

By  T.  P.  Pembertox,  formerly  Associate  Editor  of  the  "  Technologist ; " 
Author  of  "The  Student's  Illustrated  (iuide  to  Practical  Draughting."  AVith 
an  appendix  containing  the  famous  papers  by  Whitworth  '■  On  Plane  Me- 
tallic Surfaces  or  True  Planes;"  "On  an  I'niform  System  of  Screw  Threads;  " 
"Address  to  the  Institution  of  Mechanical  Engineers,  Glasgow;"  "On 
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We  have  here  a  sprightly,  fascinating  book,  "ull  of  valuable  hints,  interesting 
anecdotes  and  sharp  sayings.  It  is  not  a  compilation  of  dull  sermons  or  dry 
matliematics,  but  a  live,  readable  book.  The  papers  by  Whitworth,  now  flrsi 
made  accessible  to  the  Amei'ican  reader,  form  the  basis  of  our  modern  systems 
of  accurate  Avork. 

How  to  Use  The  Microscope. 

ByJoHX  PHiy.  Fifth  Edition-'  Greatly  enlarged,  with  over  eighty  Illustra- 
tions in  the  Text,  and  six  full  page  Engravings,  printed  on  heavy  tint 
paper.    Cloth,  Gilt, $1.00 

This  is  not  a  book  describing  ivhul  niuy  he  seen  by  the  microscope,  but  a  simple 
and  practical  work,  telling  how  to  use  the  instrument  in  its  application  to  the 
arts.  It  has  been  prepared  for  the  use  of  those  who,  having  no  knowledge  of 
the  use  of  the  microscope,  or,  indeed,  of  any  scientific  api)aratus.  desire  simple 
and  practical  instruction  in  the  best  methods  of  manairing  the  instrument  and 
preparing  objects. 


A  New  Book  for  Bee-Keepers. 

A  Dictionary  of  Practical  Apiculture,  giving  the  correct  meaning  of  nearly 
Five  Hundred  Terms,  according  to  tlie  usage  of  the  best  writers.  Intended 
as  a  Guide  to  Uniformity  of  Expression  amongst  Bee-Keepers.  With  Nu- 
merous Illustrations,  Notes,  and  Practical  Hints.  By  John  Phin,  Author 
of  "How  to  Use  the  Microscope,"  etc.  Editor  of  the  "Young  Scientist." 
Price,  Cloth,  Gilt, 50  cts. 

This  work  gives  not  only  the  correct  meaning  of  five  hundred  difl'e rent  words, 
specially  used  in  bee-keeping,  but  an  immense  amotint  of  valuable  information 
luider  tiie  different  headings.  The  lal)or  expended  ui)on  it  has  been  very  great, 
tlie  detinitions  having  been  gathered  from  the  mode  in  which  the  words  are 
used  by  our  best  writers  on  bee-keeping,  and  from  the  Imperial,  Richardson's, 
Skeat's,  Websters,  Worcester's  and  other  English  Dictionaries.  The  technical 
information  relating  to  matters  connected  with  bee-keeping  has  been  gathered 
from  the  TechnicarDictionaries  of  Brande,  Muspratt,  Ure,  Wagner,  Watts,  and 
others.  Under  the  heads  Bee.  Comb,  Glucose,  Honey,  Race,  Species.  Sugar,  Wax 
and  others,  it  brings  together  a  large  number  of  important  fads  aiid  figures 
wliich  are  now  scattered  tlu-ough  our  bee-literature,  and  through  cost  ly  scientific 
works,  and  are  not  easily  found  when  wanted.  Here  they  can  be  referred  to  at 
once  under  the  proper  liead. 

How  to  Become  a  Good  Mechanic. 

Intended  as  a  Practical  Guide  to  Self-taught  Men  ;  telling  What  to  Study  ; 
What  Books  to  Use  ;  How  to  Begin  ;  What  Difliculties  will  be  Met ;  How  to 
Overcome  Them.  In  a  word,  how  to  carry  on  such  a  Course  of  Self-instruc- 
tion as  will  enable  the  Young  Mechanic  to  rise  from  the  bench  to  something 
higher.    Paper, 15  cts. 

This  is  not  a  book  of  "goody-goody"  advice,  neither  is  it  an  advertisement 
of  any  special  system,  nor  does  it  advocate  any  hobby.  It  givet'  plain,  i)ractical 
advice  in  regard  to  acquiring  tliat  knowledge  which  alone  can  enable  a  young 
man  engagedin  any  profession  or  occupation  connected  with  the  industrial  arts 
to  attain  a  position  higher  than  that  of  a  mere  workman. 

Cements  and  Glue. 

A  Practical  Treatise  on  the  Preparation  and  Use  of  all  Kinds  of  Cements, 
(Jlue,  and  Paste.  By  Johx  Phin,  Editor  of  the  "Young  Scientist"  and  the 
"  American  Journal  of  Microscopy."    Stiff  Covers,        -       -       -       25  cts. 

Hints  for  Painters,  Decorators  and  Paperhangers. 

Being  a  selection  of  Useful  Rules,  Data,  Memoranda,  Methods  and  Sug- 
gestions for  House,  Ship,  and  Furniture  Painting,  Paperhanging,  Gilding, 
Color  Mixing,  and  other  matters  Useful  and  Instructive  to  Painters  and 
Decorators.  Prepared  with  Special  Reference  to  the  Wants  of  Amateurs. 
By  an  Olo  Hand. 25  cts. 


Any  of  these  bonlcs  will  Ue  sent  post  Duid  to  any  address  on 
receipt  of  price. 


Shooting  on  the  Wing. 

Plain  Directions  for  Acquiring  the  Art  of  Shooting  on 
the  Wing.  With  Useful  Hints  concerning  all  that  relates 
to  Guns  and  Shooting,  and  particularly  in  regard  to  the 
art  of  Loading  so  as  to  Kill.  To  which  has  been  added 
several  Valuable  and  hitherto  Secret  Eecipes,  of  Great 
Practical  Importance  to  the  Sportsman.  By  an  Old 
Gamekeeper, 
12mo.,  Cloth,  Gilt  Title.         ...        75  cents. 


The  Pistol  as  a  Weapon  of  Defence, 

In  the  House  and  on  the  Eoad. 

12mo.,  Cloth.   -  -  -  -  .  50  cents. 

This  work  aims  to  instruct  the  peaceable  and  law-abiding  citizens 
in  the  best  means  of  protecting  themselves  from  tlie  attacks  of  the 
brutal  and  the  lawless,  and  is  the  only  practical  book  published  on 
this  subject.  Its  contents  are  as  follows :  The  Pistol  as  a  Weapon  of 
Defence. — The  Carrying  of  Fire-Arms.— Different  kinds  of  Pistols  in 
Market;  How  to  Choose  a  Pistol.— Ammunition,  different  kinds; 
Powder,  Caps,  Bullets,  Copper  Cartridges,  etc.— Best  form  of  Bullet- 
How  to  Load.— Best  Charge  /'or  Pistols.— How  to  regulate  the 
Charge.— Care  of  the  Pistol ;  how  to  Clean  it.— How  to  Handle  and 
Carry  the  Pistol.— How  to  Leani  to  Shoot.— Practical  use  of  the 
Pistol ;  how  to  Protect  yourself  and  how  to  Disable  your  aatagonist. 

Lightning  Rods. 

Plain  Directions  for  the  Constrtietion  and  Erection  of 

Lightning  Kods.    By  John  Phin,  C.  E.,  editor  of  "  The 

I       Young  Scientist,"  author  of  "Chemical  History  of  the 

5       Six  Days  of  the  Creation,"  etc.    Second  Edition.    En- 

'       larged  and  Fully  Illustrated. 

12mo.,  Cloth,  Gilt  Title.      -  .  -  50  cents. 

This  is  a  simple  and  practical  little  work,  intended  to  convey  just 
such  information  as  will  enable  every  property  owner  to  decide 
whether  or  not  his  buildings  are  thoroughly  protected.  It  is  nol 
written  in  the  interest  of  any  patent  or  particular  article  of  manu- 
facture, and  by  following  its  directions,  any  ordinarily  skilful  me- 
chanic can  put  up  a  rod  that  will  afford  perfect  protection,  and  that 
will  not  infringe  any  patent.  Every  owd9»'  of  a  house  or  bam  ough- 
to  procure  a  oepy. 


THE  WORKSHOP  COMPANION. 

A   Collection    oi*  lJ$«eful   and   Rclia,l>le    Recipes^ 

Rules,    Proce««se!<>,    IVIetltods,    \f^i-ink:le!«, 

and.    Practical    Hints, 

TOR  THE   MOlfSEMOl^n  »lJVn    THE  SHOP. 


CONTENTS. 

Abyssinian  Gold;— Accidents,  General  Rules; — Alabaster,  how  to  work,  polish  and 
clean; — Alcohol; — Alloys,  rules  for  making,  and  26  recipes; — Amber,  how  to  work, 
polish  and  mend; — Annealing  and  Hardening  glass,  copper,  steel,  etc.; — Arsenical 
Soap; — Arsenical  Powder: — Beeswax,  how  to  bleach; — Blackboards,  how  to  make; — 
Brass,  how  to  work,  polish,  color,  varnish,  whiten,  deposit  by  electricity,  clean,  etc., 
etc.;  —Brazing  and  Soldering; — Bronzing  brass,  wood,  leather,  etc.; — Burns,  how  to 
cure: — Case-hardening; — Catgut,  how  prepared; — -Cements,  general  rules  for  using,  and 
56  recipes  for  preparing; — Copper,  working,  welding,  depositing; — Coral,  artificial; — 
Cork,  working; — Crayons  for  l?lackboards  ; — Curling  brass,  iron,  etc.; — Liquid  Cu- 
ticle;— Etching  copper,  steel,  glass; — Eye,  accidents  to; — Fires,  to  prevent; — Clothes  on 
Fire; — Fireproof  Dresses; — Ely  Papers; — Freezing  Mixtures,  6  recipes; — Fumigating 
Pastils; — Gilding  metal,  leather,  wood,  etc.; — Glass,  cutting,  drilling,  turning  in  the 
lathe,  fitting  stoppers,  removing  tight  stoppers,  powdering,  packing,  imitating  ground 
glass,  washing  glass  vessels,  etc.  ; — Grass,  Dry,  to  stain  ; — Guns,  to  make  shoot  close, 
to  keep  from  rusting,  to  brown  the  barrels  of,  etc.,  etc.; — Handles,  to  fasten ;— Inks, 
rules  for  selecting  and  preserving,  and  34  recipes  for; — Ink  Eraser; — Inlaying; — Iron, 
forging,  welding,  case-hardening,  zincing,  tinning,  do.  in  the  cold,  brightening,  etc., 
etc. ; — ivory,  to  work,  polish,  bleach,  etc.  ; — Javelle  Water; — Jewelry  and  Gilded  Ware, 
care  of,  cleaning,  coloring,  etc.  ; — Lacquer,  how  to  make  and  apply; — Laundry  Gloss; — 
Skeleton  Leaves; — Lights,  signal  and  colored,  also  for  tableaux,  photography,  etc.,  25 
recipes; — Lubricators,  selection  o'',  ■!  recipes  for; — Marble,  working,  polishing,  clean- 
ing;— Metals,  polishing  ; — Mirrors,  care  of,  to  make,  pure  silver,  etc.,  etc.; — Nickel, 
to  plate  with  without  a  battery; — Noise,  prevention  of; — Painting  Blight  Metals; — 
Paper,  adhesive,  barometer,  glass,  tracing,  transfer,  waxed,  etc.; — Paper,  to  dean,  take 
creases  out  of,  remove  water  stains,  mount  drawing  paper,  to  prepare  for  varnishing, 
etc  ,  etc. ; — Patina; — Patterns,  to  trace; — Pencils,  inde'ible; — Pencil  Marks,  to  fix; — 
Pewter; — Pillows  for  Sick  Room,  cheap  and  good; — Pla-'.ier-of-Paris,  how  to  work  ; — 
Poisons,  antidotes  for,  12  recipes; — Polishing  Powders,  preparation  and  use  of  (six 
pages); — Resins,  their  properties,  etc.; — Saws,  how  to  sharpen; — Sieves; — Shellac, 
properties  and  uses  of; — Silver,  properties  of,  oxidized,  old,  cleaning,  to  remove  ink 
stains  from,  to  dissolve  from  plated  goods,  etc.,  etc.  ; — Silvering  metals,  leather,  iron, 
etc.  ; — Size,  preparation  of  various  kinds  of; — Skins,  tanning  and  curing,  do  with  hair 
on; — Stains,  to  remove  from  all  kinds  of  goods; — Steel,  tempering  and  working  (six 
pages); — Tin,  properties,  methodsof  working; — Varnish,  21  recipes  for; — Varnishing, 
directions  for; — Voltaic  Batteries; — Watch,  cave  of; — Waterproofing,  7  recipes  for; — 
Whitewash; — Wood  Floors,  waxing,  staining;,  and  polishing; — Wood,  polishing; — 
Wood,  staining,  17  recipes; — Zinc,  to  pulverize,  black  varnish  for. 

164  closely-printed  pages,  neatly  bound.     Sent  bv  mail  for  36  cents 
(postage  stamps  received). 


THE  OARPENTEE'S  AND  JOINER'S 

POCKET     COMPANION. 

CONTAINING    RULES,    DATA    AND    DIRECTIONS    FOR    LAYING   OUT 
WORK  AND  FOR  CALCULATING  AND  ESTIMATING. 

Compiled  by  THOMAH  MOLONEY,  Carpenter  and  Joiner. 

Neatly  Bound  in  Cloth,  with  Gilt  Stamp  and  Red  Edges,         -         SO  cents. 

This  is  a  compact  and  hantly  little  volume,  containing  the  most  useful  rules 
and  memoranda,  collected  from  some  of  tlie  best  architectural  works  of  the  day, 
and  practically  tested  by  many  years'  experience  in  the  shop,  factory  and  build- 
ing ;  it  also  contains  a  treatise  on  the  Framixg  Square.  It  is  by  a  thoroughly 
practical  man,  and  contains  enough  matter  that  is  not  easily  found  anywhei-e 
else  to  make  it  worth  more  than  its  price  to  every  intelligent  carpenter. 

HINTS  AND   AIDS 

IN 

BUILDING    AND     ESTIMATING. 


Gives  Hints,  Prices,  tells  how  to  Measure,  explains  Btxilding 
Terms,  and,  in  short,  contains  a  fund  of  information  for  all  who 
are  interested  in  Building. 

Paper,      ------       25  cents. 

THE  A  B  c  OF  BEE  CULTURE. 

By  A.  I.  ROOT,  Editor  of  ''(ileanin^s  in  Bee  Culture." 


This  is  a  large  octavo  of  about  350  pages.  It  contains  the 
simplest  directions  of  any  book  on  Bee-keeping,  and  it  is  full  of 
practical  rules  in  every  department.  Gives  complete  directions 
for  making  Hives  and  all  kinds  of  stiiiplies  used  in  the  Apiary ; 
cuts  and  descriptions  of  plants,  and  mtxch  else,  all  arranged  in 
alphabetical  order,  so  that  any  subject  may  be  referred  to  in- 
stantly. The  iirice  is  remarkably  low,  viz.,  $1.25,  Jiandsomely 
and  strongly  bound  in  cloth,  with  gilt  title. 

Sent  l>y  Mail  on  Receipt  ofPi-ice. 

INDUSTRIAL  PUBLICATION  CO., 

Sl>-1:    Broad-vvjvy,     N"t»\v    "VTork. 


JUST  THE  BOOK  THAT  YOU  WANT 

IF  YOU  ARE  GOma  TO  BUILD  A  CHEAP 
AND   COMFORTABLE  HOME. 


BUCK'S  COTTAGE 

OTHER    DESIGNS. 

It  shows  a  great  variety  of  cheap  and  medium-priced  Cottages, 
besides  a  number  of  useful  hints  and  suggestions  on  the  various 
questions  hable  to  arise  in  building,  such  as  selections  of  site, 
general  arrangement  of  the  plans,  sanitary  questions,  etc. 

Bound  in  Paper,  Price  50  Cents. 

Cottages  costing  from  $500  to  $5,000  are  shown  in  consider- 
able variety,  and  nearly  every  tas'J'e  can  be  satisfied. 


FORTY  DESIGNS  ^ok  FIFTY  CENTS. 


The  information  on  site,  general  arrangement  of  plan,  sanitary 
matters  etc.,  etc.,  is  worth  a  great  deal  more  than  the  cost  of  the 
book. 

Will  be  sent  to  any  address  in  the  United  States  or  Canada, 
post-paid,  on  receipt  of  price.     Address 

INBUSTRIAL  PUBLICATION  CO., 

294  Broadway  New  York. 


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